It is given that Cos(A) = 1/4 and Sin(B) = 1/2
Where A is in the 3rd quadrant and B is in the 2nd quadrant
a) Find value of Sin(A)
b) Find Value of Cos(A)
c) Find value of cos(A + B) and cos (A - B)
d) Find Value of Sin(A + B) and sin (A - B)
e) What is the quadrant of A + B and A - B
f) Find the value of Sin(2A + 2B)
Answers
The answers for the following trigonometric functions are:
a) Sin(A)=√15/4
b) Cos(A)=1/4
c) Cos(A+B)=(√3-√15)/8
Cos (A- B)=(√3+15)/8
d) Sin(A+ B) =(3√5+1)/8
Sin (A- B)==(3√5-1)/8
e) The quadrant of A+B and A-B is 4th quadrant
f) Sin(2A + 2B)= (√15-6√5+4√3)/8
What are trigonometric functions?The trigonometric functions in mathematics are real functions that link the angle of a right-angled triangle to the ratios of two side lengths. They are also known as circular functions, angle functions, or goniometric functions. They are widely employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many more. Because they are some of the most basic periodic functions, Fourier analysis is frequently employed to examine periodic events.
The sine, cosine, and tangent are the trigonometric functions that are most frequently utilized in contemporary mathematics.
Given,
Cos(A) = 1/4 and Sin(B) = 1/2
4=√1+x²
1+x²=16
x²=15
x=√15
4=1+x²
x²=3
x=√3
a) Sin(A)=√15/4
Sin(B)=1/2
b) Cos(A)=1/4
Cos(B)=√3/2
c) Cos(A+B)=CosACosB-SinASinB
=(1/4)(1/2)-(√15/4)(1/2)
=(√3-√15)/8
Cos(A-B)=CosACosB+SinASinB
=(1/4)(√3/2)+(√15/4)(1/2)
=(√3+15)/8
d) Sin(A+B)+SinACosB+CosASinB
=(√15/4)(√3/2)+(1/4)(1/2)
=(3√5+1)/8
Sin(A-B)=SinACosB-SinBCosA
=(√15/4)(√3/2)-(1/4)(1/2)
=(3√5-1)/8
e) The quadrant of A+B and A -B is 4th quadrant.
f) Sin(2A+2B)=Sin2ACos2B+Cos2ASin2B
=(√15/8)(1-√3)+((4-√15)/4)(√3/2)
=(√15-3√5+4√3-3√5)/8
=(√15-6√5+4√3)/8
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Related Questions
Question 12 (5 points)
Jamal purchased parts for his car. The parts cost $285, but he used a coupon and the
new price was $228. How much of a discount did Jamal get by using a coupon?
57%
2%
80%
20%
O
Answers
Answer:
20%
Step-by-step explanation:
the discount: 285-228=$57
percentage of the discount: 57/285 x 100=20%
John wishes to choose a combination of two types of cereals for breakfast - Cereal A and Cereal B. A small box (one serving) of Cereal A costs $0.50 and contains 10 units of vitamins, 5 units of minerals, and 15 calories. A small box (one serving) of Cereal B costs $0.40 and contains 5 units of vitamins, 10 units of minerals, and 15 calories. John wants to buy enough boxes to have at least 500 units of vitamins, 600 units of minerals, and 1200 calories. How many boxes of each cereal should he buy to minimize his cost?
Answers
Let's assume that John buys x boxes of Cereal A and y boxes of Cereal B. Then, we can write the following system of inequalities based on the nutrient and calorie requirements:
10x + 5y ≥ 500 (minimum 500 units of vitamins)
5x + 10y ≥ 600 (minimum 600 units of minerals)
15x + 15y ≥ 1200 (minimum 1200 calories)
We want to minimize the cost, which is given by:
0.5x + 0.4y
This is a linear programming problem, which we can solve using a graphical method. First, we can rewrite the inequalities as equations:
10x + 5y = 500
5x + 10y = 600
15x + 15y = 1200
Then, we can plot these lines on a graph and shade the feasible region (i.e., the region that satisfies all three inequalities). The feasible region is the area below the lines and to the right of the y-axis.
Next, we can calculate the value of the cost function at each corner point of the feasible region:
Corner point A: (20, 40) -> Cost = 20
Corner point B: (40, 25) -> Cost = 25
Corner point C: (60, 0) -> Cost = 30
Therefore, the minimum cost is $20, which occurs when John buys 20 boxes of Cereal A and 40 boxes of Cereal B.
ILL GIVE BRAINLEST, Find the value of x.
Answers
Answer:
x=6, y=128
set 5x+16 = 7x+4
-2x=-12
x=6
plug x into equation= 46
180-46=134
y+6=134
y=128
Answer:
x= 45 Degrees
Step-by-step explanation:
Total Triangle= 180 Degrees
Subtract Right Angle: 180-90= 90 Degrees
Divide by 2 because it is an isosceles triangle: 90/2= 45 Degrees
John has a savings account that pays him a compounded interest rate of 10%. The interest rate is compounded monthly. His starting principal is $1,604.00. What is his second month's interest?
Answers
John's second month's interest, given his starting principal and the interest rate, is $13.48
How to find the second interest?First, find the monthly interest rate as the savings account is compounded monthly:
= 10% / 12 months per year
= 10/12 %
The amount after the first month would be:
= 1, 604 x ( 1 + 10/12%)
= $1, 617.37
The second month's interest to John is therefore:
= 1, 617. 37 x 10/12%
= $13.48
In conclusion, in the second month of his savings investment, John would make an interest of $13.48.
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Heyyyy can someone help me ?? is for today ;-;
Zuleima puts her pebbles on the table. Make groups of 3 and have 1 left. Then make groups of 5 and have 2 left. How many stones does Zuleima have?
a) 32 b) 10 c) 26 d) 1000 e) 22
Answers
Answer:
E) 22
Step-by-step explanation:
To solve this, use process of elimination. (If they are both '☆'s, it is the answer.)
A)32
3n+1 x 5n+2 ☆
B) 10
3n+1 ☆ 5n+2 x
C) 26
3n+1 ☆ 5n+2 x
D) 1000
3n+1 ☆ 5n+2 x
E) 22
3n+1 ☆ 5n+2 ☆
The answer is E) 22
Find y'' by implicit differentiation: \(9x^2+y^2=4\)
Answers
y" for the equation is -(9+\((y')^{2}\))/y
Implicit differentiation is the type of differentiation where you differentiate the whole equation with respect to a particular variable.
For the given equation,
\(9x^{2} +y^{2}=4\)
On differentiating both sides with respect to x, we get
\(\frac{d}{dx} (9x^{2} ) + \frac{d}{dx} y^{2} = \frac{d}{dx}(4)\)
\(9\frac{d}{dx}x^{2} + \frac{d}{dx}y^{2} = 0\)
(Since the differential of a constant is 0)
9(2x) + 2y*y' = 0
18x + 2y*y' = 0
On differentiating both sides with respect to x, we get
\(\frac{d}{dx}(18x) + \frac{d}{dx}(2y*y') = 0\)
18 + 2(y')^2 + 2y*y'' = 0
(By using UV rule of differentiation)
y'' = -(9+\((y')^{2}\))/y
Therefore, by implicit differentiation, y'' = -(9+\((y')^{2}\))/y
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Find the value of the test statistic for testing whether there is a linear relationship between the and the estimated number. Round your answer to two decimal places, if necessary.
Answers
the value of the test statistic for testing whether there is a linear relationship between the and the estimated number is 0.3506905
Using a correlation Coefficient calculator, the correlation Coefficient, r for the data = 0.127
The test statistic :
T = r² / √(1 - r²) / (n - 2)
Sample size, n = 10
Hence,
T = 0.127² / √(1 - 0.127²) / (10 - 2)
T = (0.016129 / 0.3506905)
T = 0.3506905
The value of the test statistic to 2 decimal places is 0.35
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dice is rolled 3000 times
how many times would you expect to roll a 5
Answers
Answer:
500 times
Step-by-step explanation:
3000/6
HEY. YES, YOU. PLEASE HELP
Answers
Answer:
its a
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
Tis' a function because for each input, there's one output. Because, for any given x, there is only 1 sin(x).
Solve the equation for all real solutions 8m^2 - 6m - 9 = 0
Answers
What is -20/2(7 2/3)
Answers
The simplified form of -20/2(7 2/3) is -230/3.
To solve the expression -20/2(7 2/3), we need to follow the order of operations, which states that we should perform the operations inside parentheses first, then any multiplication or division from left to right, and finally any addition or subtraction from left to right.
First, let's convert the mixed number 7 2/3 to an improper fraction.
7 2/3 = (7 * 3 + 2) / 3 = 23/3
Now, let's substitute the value back into the expression:
-20/2 * (23/3)
Next, we simplify the multiplication:
-10 * (23/3)
To multiply a fraction by a whole number, we multiply the numerator by the whole number:
-10 * 23 / 3
Now, we perform the multiplication:
-230 / 3
Therefore, the simplified form of -20/2(7 2/3) is -230/3.
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A manufacturer has 576 square inches of material available to construct the 6 faces of a carton, which will be in the shape of a rectangular prism. To maximize the volume, the carton will have dimensions such that the length and width are each twice the height.
Answers
To maximize the volume, of the rectangular prism, the carton should have dimensions of approximately 10.74 inches (length), 10.74 inches (width), and 5.37 inches (height).
What is the dimension required to maximize the volume of the box?Assuming the height of the rectangular prism is h inches.
According to the given information, the length and width of the prism will be twice the height, which means the length is 2h inches and the width is also 2h inches.
The total surface area of the rectangular prism is given by the formula:
Surface Area = 2lw + 2lh + 2wh
Substituting the values, we have:
576 = 2(2h)(2h) + 2(2h)(h) + 2(2h)(h)
576 = 8h² + 4h² + 4h²
576 = 16h² + 4h²
576 = 20²
h² = 576/20
h² = 28.8
h = √28.8
h = 5.37
The height of the prism is approximately 5.37 inches.
The length and width will be twice the height, so the length is approximately 2 * 5.37 = 10.74 inches, and the width is also approximately 2 * 5.37 = 10.74 inches.
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Given the points (5, -6) and (-9, -7), find the rate of change between the points.
Answers
Answer:
- 1
-------
-14
Step-by-step explanation:
y,, - y, (-7) - ( -6 ) - 1
--------- = ---------------- = -------
x,, - x, (-9) - ( 5 ) -14
work out the perimeter of the semi-circle take pi to be 3.142
Answers
P = 25.71 cm
Step-by-step explanation:
Perimeter of semicircle = πD/2
Where D=10 cm
P = (3.142)(10)/2
P = (3.142)(5)
P = 15.71 cm
Complete Perimeter of Semicircle = P + Diameter
= 15.71 + 10
= 25.71 cm
A garden table and a bench cost $717 combined. The garden table costs $67 more than the bench. What is the cost of the bench?
Answers
Subtract the difference form the total:
717 - 67 = 650
Divide the remaining amount by 2:
650/2 = 375
The bench cost$375
Which of the following is the equation of a line with a slope of -5/9
Answers
Answer:
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Please help me important question in image
Step-by-step explanation:
Please help me important question Please help me important question in image
in image
Please help me iPlease help me important question in image
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jose has 3 genres of songs on his Mp3 player. Half of the songs are country songs. A fourth of the songs are rock. The other 10 songs are jazz. If his MP3 player is playing songs at random and on repeat, what is the probability that it will play a rock song followed by a country song
Answers
Answer:
because he has the rock next to the country song
Let's roll two dice and find the probability of rolling a certain sum. Is this a simple or compound event?
Two dice - Red and Blue
Recall that a simple event has one and only one outcome of interest. In this example, we are rolling two dice, but we are only interested in one outcome, the sum of the two dice. This is a simple event.
What is the probability of:
Rolling a sum of 1?
Rolling a sum of 3?
Rolling a sum of 12?
Rolling a sum of 7?
Since we are rolling a pair of dice and looking for the sum, the sample space is a little more complicated than rolling one die. The chart below will help us determine the possible outcomes. The top row indicates the numbers on the sides of the blue die and the first column represents the number on the sides of the red die. The white area indicates the sum of the numbers in the row and column.
# Rolled 1 2 3 4 5 6
1 1+1=2
1
+
1
=
2
1+2=3
1
+
2
=
3
1+3=4
1
+
3
=
4
1+4=5
1
+
4
=
5
1+5=6
1
+
5
=
6
1+6=7
1
+
6
=
7
2 2+1=3
2
+
1
=
3
2+2=4
2
+
2
=
4
2+3=5
2
+
3
=
5
2+4=6
2
+
4
=
6
2+5=7
2
+
5
=
7
2+6=8
2
+
6
=
8
3 3+1=4
3
+
1
=
4
3+2=5
3
+
2
=
5
3+3=6
3
+
3
=
6
3+4=7
3
+
4
=
7
3+5=8
3
+
5
=
8
3+6=9
3
+
6
=
9
4 4+1=5
4
+
1
=
5
4+2=6
4
+
2
=
6
4+3=7
4
+
3
=
7
4+4=8
4
+
4
=
8
4+5=9
4
+
5
=
9
4+6=10
4
+
6
=
10
5 5+1=6
5
+
1
=
6
5+2=7
5
+
2
=
7
5+3=8
5
+
3
=
8
5+4=9
5
+
4
=
9
5+5=10
5
+
5
=
10
5+6=11
5
+
6
=
11
6 6+1=7
6
+
1
=
7
6+2=8
6
+
2
=
8
6+3=9
6
+
3
=
9
6+4=10
6
+
4
=
10
6+5=11
6
+
5
=
11
6+6=12
6
+
6
=
12
How many outcomes are in the sample space? Answer
Answers
Answer:
the answer to your question how many outcomes is really gonn adepend on you you slove you problem but my amswer is gonna be 7.
In one weekend, a theatre sells 61,366 tickets to a new movie. Write the values for each of the 6s in 61,366.
The values of the 6s are
Answers
Answer:
60,000, 60, 6.
Step-by-step explanation:
just separate the numbers into sections and boom
what is the difference between -15-9?
Answers
Answer:
Step-by-step explanation:
-15-9 = -24
I would think about it as adding 15 and 9, but just make the answer negative.
Why can you use fraction multiplication to check the
answer to a fraction division problem? How do you use
multiplication to check a division problem?
Answers
Answer:
Division and multiplication are inverse operations. This means they "undo" each other. You can check your answer by multiplying the quotient by the divisor. You should get the dividend.
have a great day :)
Because multiplication is the converse of division,
If x/y=z then x=?x/y=z
x=yz
Division and multiplication are inverse operations. This means they "undo" each other. You can check your answer by multiplying the quotient by the divisor. You should get the dividend.
Just like addition is the converse of subtraction.
If x/y=z,
then x=yz.
If x divided by y is equal to z, then x equals y times z. These are the rules of arithmetic. If they weren't true the universe would fall apart! The rule can be used as a check that you have the right answer.
Therefore converse of division is the answer.
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The members of a youth dance company were asked their favorite ice cream flavors for
an upcoming party to celebrate a competition win. The results are displayed in the bar
graph below.
Based on the information in the graph, which of the following statements are true?
Choose one. 10 points
Favorite Ice Cream Flavors
10
8
6
Amount
4
2
0
Vanilla - 6
Strawberry - 5
Cookies & Cream - 9
Butter pecan - 3
Chocolate - 2
Answers
Answer:
2
Step-by-step explanation:
ASAP! GIVING BRAINLIEST! Please read the question THEN answer correctly! No guessing.
Answers
Answer:
Step-by-step explanation:
f(x) = x^2
reflect along the x-axis
g(x) = -x^2
expand vertilcally by a factor of 1/3
g(x) = (-1/3) x^2
move horizontally 4 units to the left
g(x) = (-1/3) (x+4)^2
hope this helps
Answer:
B. The graph of G(x) is the graph of F(x) stretched vertically, flipped over the x-axis, and shifted 4 units to the left.
Step-by-step explanation:
The \(\frac{-1}{3}\) is less than one, making it stretch wider, and the (-) made it flip over the x-axis. The +4 in \((x+4)^2\) made the function on the graph shift 4 units to the left.
This makes the correct answer be "B."
solve the equation 3x < 18
Answers
Answer:
x < 6
Step-by-step explanation:
3x < 18 ( divide both sides by 3 )
x < 6
Which of the following expressions is an equivalent factored form for the expression (4x^(3)+49x)
Answers
The equivalent factored form for the expression; (4x³ + 49x) as in the task content is; x(4x² +49).
What is the equivalent factored form for the expression (4x³ + 49x)?It follows from the task content that the expression; (4x³ + 49x) be factored to result in its factored form expression.
Hence, one must determine the greatest common factor of thee terms; 4x³ and 49x.
In this case, only x is a common factor and hence, the factored form for the expression is;
x (4x² +49).
Ultimately, the equivalent factored form for the expression; (4x³ + 49x) as in the task content is; x(4x² +49).
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A bag contains two red marbles, four green ones, one lavender one, two yellows, and two orange marbles. HINT [See Example 7.] How many sets of five marbles include either the lavender one or exactly one yellow one but not both colors?
Answers
There are 2518 sets of five marbles that include either the lavender one or exactly one yellow one, but not both.
To solve this problem, we need to find the number of sets of five marbles that include either the lavender one or exactly one yellow one, but not both colors. Here's one way to approach the problem:
Number of sets of five marbles that include the lavender one: There is only one lavender marble, so we can choose any 4 other marbles to go with it.
There are a total of 7 marbles to choose from, so there are 7 possible choices for the first marble, 6 for the second, 5 for the third, and 4 for the fourth.
This gives us a total of 7 x 6 x 5 x 4 = 840 possible sets of five marbles that include the lavender one.
Number of sets of five marbles that include exactly one yellow one: There are two yellow marbles,
So there are 2 possible choices for the yellow marble. For each choice, we can choose any 4 other marbles to go with it.
As before, there are 7 marbles to choose from, so there are 7 possible choices for the first marble, 6 for the second, 5 for the third, and 4 for the fourth.
This gives us a total of 2 x (7 x 6 x 5 x 4) = 1680 possible sets of five marbles that include exactly one yellow one.
Number of sets of five marbles that include both the lavender one and exactly one yellow one:
We need to subtract these sets from the total number of sets that include either the lavender one or exactly one yellow one.
We have already found that there are 840 sets of five marbles that include the lavender one, and 1680 that include exactly one yellow one.
To find the number of sets that include both, we can choose any one yellow marble and the lavender one.
There are 2 choices for the yellow marble and 1 choice for the lavender one,
So there are 2 x 1 = 2 possible sets of five marbles that include both the lavender one and exactly one yellow one.
Number of sets of five marbles that include either the lavender one or exactly one yellow one, but not both:
Finally, we need to subtract the number of sets that include both the lavender one and exactly one yellow one from the total number of sets that include either the lavender one or exactly one yellow one.
The total number of sets that include either the lavender one or exactly one yellow one is 840 + 1680 = 2520. The number of sets that include both is 2,
So the number of sets that include either the lavender one or exactly one yellow one, but not both, is 2520 - 2 = 2518.
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which statement correctly describes the relation between the variable in the equation C = nd
Answers
Answer:
nd is c
Step-by-step explanation:
Find the volume plzzzzz thx
Answers
Answer:
144 isnt it? 6x6x4 length x width x height it should be 36x4
Step-by-step explanation i dont know sorry
What is the slope of a line that is perpendicular to the line whose equation is 7x−3y=10?A. −7/3B. 3/5C. −3/7D. 3/7
Answers
The line given is
\(7x-3y=10\)The equation expressed in slope-intercept is now;
\(\begin{gathered} 7x-3y=10 \\ Subtract\text{ 7x from both sides of the equation;} \\ 7x-7x-3y=10-7x \\ -3y=10-7x \\ \text{Divide both sides by -3} \\ -\frac{3y}{-3}=\frac{10-7x}{-3} \\ y=-\frac{10}{3}-\frac{7}{-3}x \\ y=-\frac{10}{3}+\frac{7}{3}x \end{gathered}\)Note that the slope of this line is the coefficient of x and that is
\(\frac{7}{3}\)The slope of the line perpendicular to this one would be a negative inverse and that now gives us;
\(\begin{gathered} \text{Inverse}=\frac{3}{7} \\ \text{Negative inverse}=-\frac{3}{7} \end{gathered}\)The slope of the line perpendicular is option C, (that is -3/7)
The amount of money in an account may increase due to rising stock prices and decrease due to falling stock prices. Maggie is studying the change in the amount of money in two accounts, A and B, over time.
The amount f(x), in dollars, in account A after x years is represented by the function below:
f(x) = 9,628(0.92)x
Part A: Is the amount of money in account A increasing or decreasing and by what percentage per year? Justify your answer.
Part B: The table below shows the amount g(r), in dollars, of money in account B after r years.
r (number of years) 1 2 3 4
g(r) (amount in dollars) 8,972 8,074.80 7,267.32 6,540.59
Which account recorded a greater percentage change in amount of money over the previous year? Justify your answer.
Answers
The amount of money in account A is decreasing by 8% per year.
The account that recorded a greater percentage change in amount of money over the previous year is account B.
How to calculate the percentage?From the information, the amount f(x), in dollars, in account A after x years is represented by the function below:
f(x) = 9,628(0.92)x
Therefore, this shows a decrease and the percentage will be:
= 1 - 0.92
= 0.08
= 8%
The account that recorded a greater percentage change will be:
Account B = (8,972 - 8,074.80) / 8,972 × 100
= 10%
Therefore, B has a higher percentage.
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