a point on the terminal side of angle theta is given. Find the exact value of each of the six trigonometric functions of theta. given point- (3,7)
Answers
Given point: (3,7)
Opposite side: O
Adjacent side: A
Hypotenuse: H
\(\begin{gathered} O=7 \\ A=3 \\ \end{gathered}\)Use pythagorean theorem to find H:
\(\begin{gathered} H=\sqrt[]{A^2+O^2} \\ H=\sqrt[]{3^2+7^2} \\ H=\sqrt[]{9+49} \\ H=\sqrt[]{58} \end{gathered}\)Trigonometric functions:
\(\begin{gathered} \sin \theta=\frac{O}{H}=\frac{7}{\sqrt[]{58}} \\ \\ \text{Razionalizing the denominator;} \\ \sin \theta=\frac{7}{\sqrt[]{58}}\cdot\frac{\sqrt[]{58}}{\sqrt[]{58}}=\frac{7\sqrt[]{58}}{58} \end{gathered}\)\(\begin{gathered} \cos \theta=\frac{A}{H}=\frac{3}{\sqrt[]{58}}_{} \\ \\ \text{Razionalizing the denominator:} \\ \cos \theta=\frac{3}{\sqrt[]{58}}_{}\cdot\frac{\sqrt[]{58}}{\sqrt[]{58}}=\frac{3\sqrt[]{58}}{58} \end{gathered}\)\(\tan \theta=\frac{O}{A}=\frac{7}{3}\)\(\begin{gathered} \\ \csc \theta=\frac{H}{O}=\frac{\sqrt[]{58}}{7} \end{gathered}\)\(\sec \theta=\frac{H}{A}=\frac{\sqrt[]{58}}{3}\)\(\cot \theta=\frac{A}{O}=\frac{3}{7}\)
Related Questions
Do you take the free samples offered in super- markets? About 70% of all customers will take free samples. Furthermore, of those who take the free samples, about 30% will buy what they have sampled. Suppose you set up a counter in a supermarket offering free samples of a new product. The day you are offering free samples, 317 customers pass by your counter.
Answers
Answer:
222 customers took a free sample of the product, and 67 finally bought it.
Step-by-step explanation:
Given that 317 consumers passed through the sample stand, and taking into account that 70% usually take free samples, the number of people who take free samples is determined by the following calculation:
317 x 70/100 = X
22,190 / 100 = X
221.9 = X
Therefore, of the 317 consumers, about 222 took free samples of the product. Furthermore, of those 222, it is estimated that 30% bought the product after testing the sample. To determine the number of people who bought the product, the following calculation must be made:
222 x 30/100 = X
6,660 / 100 = X
66.6 = X
Therefore, 67 consumers purchased the product after taking a free sample of it.
Chilling and Dying.
Same nights every night.
The pandemic got to go no cap.
Answers
Answer:
yes
Step-by-step explanation:
yes
very poetic
What is the difference?
-3 2/3 - (-2 1/4)
Answers
let's firstly convert the mixed fractions to improper fractions.
\(\stackrel{mixed}{3\frac{2}{3}}\implies \cfrac{3\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{11}{3}}~\hfill \stackrel{mixed}{2\frac{1}{4}} \implies \cfrac{2\cdot 4+1}{4} \implies \stackrel{improper}{\cfrac{9}{4}} \\\\[-0.35em] ~\dotfill\\\\ -\cfrac{11}{3}-\left( \cfrac{9}{4} \right)\implies -\cfrac{11}{3}+\cfrac{9}{4}\implies \cfrac{-(4)11~~ + ~~(3)9}{\underset{\textit{using this LCD}}{12}} \\\\\\ \cfrac{-44+27}{12}\implies \cfrac{-17}{12}\implies {\Large \begin{array}{llll} -1\frac{5}{12} \end{array}}\)
PLEASE ONLY ANSWER IF CORRECT!! Please do not answer if you are not sure, it is important to me.
Answers
Answer:
16v+1 pls brainliest!
Evaluate each expression.
Answers
Answer:
THIS DESERVES A BRAINLIEST BECAUSE I PUT ALL OF THE ANSWERS AND THE WORK TO IT
1: 6
2: 3
3: 5
4: 1
5: 3
6: -1
7: 8
8: 4
9: 3
10: 16
Step-by-step explanation:
Use PEMDAS
1. (2x2)+2
You do 2x2 first which is 4 so then you do 4+2 which is 6
2. 6 divided by (5-3)
You do 5-3 first which is 2 then 6/2 (that's 6 divided by 2) which is 3
3. 6/6 x5
so you do 6 divided by 6 which is 1 then you get 1x5 which is 5.
4. 2-(5-4)
5-4 is 1 and 2-1 is 1
5. 2+6/6
6 divided by 6 is 1 and 2+1 is 3
6. (-6)+5 is -1
7. 1-(-7) is the same as 1+7 which is 8
8. (-3)-7 is the same as -3+7 which is the same as 7-3 which is 4
9. 5+(-2) is the same as 5-2 which is 3
10. 8-(-8) is the same as 8+8 which is 16
one card is drawn from a pack of 52cards each of the 52 cards being equally likely to be drawn. what is the probability that the card drawn is a king?
Answers
The probability of drawing a king from a standard deck of 52 cards is 1/13.
In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.
To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).
The total number of possible outcomes is 52 because there are 52 cards in the deck.
The favorable outcomes, in this case, are the four kings.
Therefore, the probability of drawing a king is given by:
Probability = (Number of favorable outcomes) / (Number of possible outcomes)
= 4 / 52
= 1 / 13
Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.
This means that out of every 13 cards drawn, on average, one of them will be a king.
It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.
Each draw is independent, and the probability of drawing a king is constant.
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The equation below describes a parabola. If a is negative, which way does the parabola open?
x= av?
Answers
In hyperbola, If a is negative, left does the parabola open.
What is an example of a hyperbola?
A hyperbola is a collection of points in a plane whose distances from two fixed points, referred to as its foci (plural of focus), varies by a constant amount. For instance, the picture displays a hyperbola with foci at (-3,0) and (3,0). The point at illustrates its constant distance as being 4. (-3,-2.5).
Open and closed hyperbolas are the two different varieties. A hyperbola widens on the x-axis at one end and the y-axis at the other.
The equation below describes a parabola.
x= av
If a is negative, left does the parabola open.
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what should be added to -13/25+21/5+-21/18 to get 5?
Answers
ATQ,
= \( \dfrac{ - 13}{25} + \dfrac{21}{5} + \frac{ - 21}{18} + x = 5\)
Take the lcm of 25,5,18 and then manipulate it accordingly.= \( \dfrac{ 377}{150} + x = 5\)
= \( x = 5 - \dfrac{ 377}{150}\)
= \( x = \dfrac{ 373}{150}\)
Answer
=727/150
Step-by-step explanation:
-13/25 + 21/18 + 21/18
= -13 + 105/25 + 21/18
= 92/25 + 21/18
= 1656 + 525/450
= 2181/450 = 727/150
Have nice day
Name an acute angle and give its measure.
Angle: ______ Measure: _____
Name an obtuse angle and give its measure. (2 points)
Angle: _____ Measure: _____
Name one right angle. (1 point
Name one straight angle. (1 point)
Answers
11. Angle KEF = 40°, Angle KEJ = 50°
12. Angle HEF = 115°, Angle KED = 140°
13. Angle JEF = 90°, Angle KEF = 90°
14. Angle DEF = 180°
Define the term geometry?The study of points, lines, and shapes in two and three dimensions, as well as their properties and relationships, is the focus of the mathematical discipline known as geometry.
11. Acute angles: Those angles are less than 90 degree angles.
Angle KEF = 40°
Angle KEJ = 50°
Angle KEH = 75°
Angle JEH = 25°
Angle HED = 65°
12. Obtuse angles: Those angles are more than 90 degree angles.
Angle HEF = 115°
Angle KED = 140°
13. Right angle: Those angles are 90 degree angle.
Angle JEF = 90°
Angle KEF = 90°
14. Straight angle: Those angles make 180 degree angle.
Angle DEF = 180°
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DON'T SOLVE IT
I know the answer. I just need to know the TOPIC in geometry.
What is the topic???
Answers
Answer:
Triangles in Geometry
Step-by-step explanation:
The following table shows the examination grades in Maths SL for a class of 32 students. Find the standard deviation for the results.
Answers
The standard deviation of the examination grades in Maths SL for the class would be 1. 39.
How to find the standard deviation?First, list the grades based on their frequencies to be:
2, 2, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7
Then find the mean :
= ( 2 + 2 + 3 + 3 + 4 + 4 + 4 + 4 + 4 + 4 + 5 + 5 + 5 + 5 + 5 + 5 + 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 +7 + 7 + 7 + 7 + 7 ) / 32
= 5. 125
Then find the variance :
= ( ∑ ( x - mean ) ² / number of grades )
= ((2 - 4.85)² + (2 - 4.85)² + (3 - 4.85)² + (3 - 4.85)² + (4 - 4.85)² + (4 - 4.85)² + (4 - 4.85)² + (4 - 4.85)² + (4 - 4.85)² + (4 - 4.85)² + (5 - 4.85)² + (5 - 4.85)² + (5 - 4.85)² + (5 - 4.85)² + (5 - 4.85)² + (5 - 4.85)² + (5 - 4.85)² + (6 - 4.85)² + (6 - 4.85)² + (6 - 4.85)² + (6 - 4.85)² + (6 - 4.85)² + (6 - 4.85)² + (6 - 4.85)² + (6 - 4.85)² + (6 - 4.85)² + (7 - 4.85)² + (7 - 4.85)² + (7 - 4.85)² + (7 - 4.85)² + (7 - 4.85)²) / 20
= 1. 921875
The standard deviation can be found by the formula :
σ = √Variance
= √ 1. 921875
= 1. 39
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If ΔSTU is reflected over the y-axis, what are the coordinates of the vertices of ΔS’T’U’? Drag numbers to complete the coordinates. Numbers may be used once, more than once, or not at all.
NEED HELP ASAP
Answers
Answer:S(3,2),T(2,4),U(1,1)
Step-by-step explanation:
I took the quiz and got it right
Tre was standing on the pitcher's mound. The pitcher's mound is 60.5 feet from home base.
Draw Tre's position at the pitcher's mound as the point (42.78, 42.78) on your diagram above. (1 point)
I’ll give brainliest
Answers
For pitchers in high school to the Major League, the mound is an 18-foot-diameter circle that is 10 inches above home plate.
The mound is flat and encircles the pitching rubber. Beginning six inches from the edge of the rubber and 60 feet beyond home plate, the hill slopes down at a rate of one centimetre every foot throughout an expanse of not less than six feet. In baseball, the pitcher's mound refers to the elevated area within the infield where the pitcher stands and throws.
It is termed a mound because it has a slight incline to it, similar to a small hill. Learn more about the pitching circle in baseball by reading on. The mound comprises a 18-foot-diameter rectangle standing 10 inches beyond home plate for pitchers playing in high school through the Major League.
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two planes that do not intersect are ...... parallel
Answers
Answer:
Vertical and horizontal lines are perpendicular. Two lines are parallel lines if they are coplanar and do not intersect.
Step-by-step explanation:
Lines that are not coplanar and do not intersect are called skew lines. Two planes that do not intersect are called parallel planes. hope this helps you :)
AT&T is having a sale on all cell phones. They will give you a loan to pay for the phone. Your phone costs $899 How much will you pay for the phone if they charge you 4.5% interest, and it will take you 24 months to pay it off.
-How do you do this equation?
Answers
Answer:
Its a scam AT&T has no such sale going on right now.
Step-by-step explanation:
A store sold 550 video games during the month of December. If this made up 12.5% of its yearly video games scales, about how many video games did the store sell all year?
Answers
Answer:
The store sold 4,400 video games all year.
Step-by-step explanation:
Percentages
The x percent of a number N is calculated as:
\(\displaystyle P=\frac{x}{100}*N\)
If the value of P is known, then:
\(\displaystyle N=\frac{100}{x}*P\)
We know the store sold P=550 video games during the month of December and it corresponds to the x=12% of its yearly games sales (N).
Let's calculate N:
\(\displaystyle N=\frac{100}{12.5}*550\)
N = 4,400
The store sold 4,400 video games all year.
The counting number just before C5F sixteen is
Answers
the counting number just before C5F16 is 3,072.
For each expression, select all equivalent expressions from the list.
(a) 11x-4x+5x
12x
12+x
7x-5x
7x+5x
(b) 7(1+8y)
7+8y
7+56y
7•1-+7•8y
7+1•7+8y
Selective answer choice
Answers
Answer: a
Step-by-step explanation:
7(x -5)
12 + x
Consider two points A(0,0) and B(1, 1) on a Cartesian plane. The equation of the axis of the segment AB is: A. y = 1 2 − B. y = 2 − C. y = 1 − 2 D. y = 1 − E. y = 1 − 2
Answers
So, the equation of the axis of the segment AB is (A) y = 1/2 - x/2.
What is slope?
In mathematics, slope refers to the steepness or incline of a line on a graph. It is a measure of how much the dependent variable changes for every unit change in the independent variable.
The slope of the line passing through points A and B can be calculated as follows:
slope = (change in y) / (change in x) = (1-0) / (1-0) = 1/1 = 1
The equation of a line in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
To find the y-intercept, we can use point A (0,0) and substitute the slope value.
y = mx + b
0 = 1(0) + b
b = 0
Therefore, the equation of the line passing through points A and B is:
y = 1x + 0
Simplifying, we get:
y = x
So, the answer is (A) y = 1/2 - x/2. However, this is not one of the given answer choices. We can also write the equation in point-slope form as y - y1 = m(x - x1) using point A, which gives:
y - 0 = 1(x - 0)
y = x
This confirms our earlier answer.
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In •A find CE if BA=7.35.
Answers
The value of CE is 14.7 units.
What if the diameter of a circle?The diameter of a given circle is a straight line which passes through the center of the circle and divides it into two equal semi-circles.
So that in the given circle with center A, we have;
CE = BD (diameter of a given circle)
BA = EA = CA = DA (radius of a given circle)
CE is the diameter of the circle, and BA is the radius, so that;
CE = 2*BA
= 2*7.35
= 14.7
CE = 14.7
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Meg constructed triangle POQ and then used a compass and straightedge to accurately construct line segment OS as shown in the figure.
Answers
Answer:
key
Step-by-step explanation:
Could someone help me with this question.
First Image is the answer choices for each question
Second image is the questions
Answers
9514 1404 393
Answer:
P'(-1, -4)N'(-2, 1)U'(-5, 0)Step-by-step explanation:
Reflection over the y-axis negates the x-coordinate value:
(x, y) ⇒ (-x, y)
Then the image points are ...
P(1, -4) ⇒ P'(-1, -4)
N(2, 1) ⇒ N'(-2, 1)
U(5, 0) ⇒ U'(-5, 0)
Can I please get help plsss
Answers
Answer:
1000 ft/min
Step-by-step explanation:
Rate of change in ft per min is 1000 ft per 1 minute from reading the graph
Here is an unlabeled polygon along with its scaled copies Polygons A Preach copy
determine the scale factor Explain how you know
Answers
The complete question with the unlabeled polygon and scaled copies has been attached.
Answer:
1) For polygon A; scale factor = ½
2)For polygon B; scale factor = 2
3) For polygon C; scale factor = 3/2
4) For polygon D; scale factor = 1
Step-by-step explanation:
Scale factor is defined as the ratio of the length of one side of a figure to the length of the corresponding side of another figure.
Now, from the image attached, we can see that the unlabeled polygon has 4 sides, and has a vertical height of 2 units on the left side.
1) Now, for polygon A, we can see that the vertical height on the left side has a vertical height of 1 unit.
Therefore, in relation to the unlabeled polygon, it is dilated by a scale factor of; k = 1/2
2)for polygon B, we can see that the vertical height on the left side has a vertical height of 4 units.
Therefore, in relation to the unlabeled polygon, it is dilated by a scale factor of; k = 4/2 = 2
3) for polygon C, we can see that the vertical height on the left side has a vertical height of 3 units
Therefore, in relation to the unlabeled polygon, it is dilated by a scale factor of; k = 3/2
4) for polygon A, we can see that the vertical height on the left side has a vertical height of 2 units.
Therefore, in relation to the unlabeled polygon, it is dilated by a scale factor of; k = 2/2 = 1
Answer:
2
Step-by-step explanation:
Anyone know the answer?
0.08m^3 to kg
Answers
Answer:
hush Nikki
nnnnmm
nnnnn
Question 3 of 10 Use the drawing tool(s) to form the correct answers on the provided graph. Greph the lines that represent the following system of linear equations, 2x + 1.5y = -60, 2x + y = -50 Then, mark the point on the graph that represents the solution to the system.
Answers
We are asked to graph the following system of equations:
\(\begin{gathered} 2x+1.5y=-60 \\ 2x+y=-50 \end{gathered}\)The graph of both equations are lines, as follows:
The point of interception is the solution to the system of equations.
Find value of x with proofs
Answers
In response to the given question, we can state that Therefore, the value equation of x is 30 degrees.
What is equation?A algebraic equation is a technique that links two statements and utilises the equals sign (=) to express equivalence. In algebra, an equation refers to the mathematical statement that proves the equality of two formulas. For example, in the computation 3x + 5 = 14, a normalise inserts a gap between the numbers 3x + 5 and 14. A mathematical formula may be used to explain the link between the two phrases written on either side of a letter. The emblem and the programme are usually the same. For example, 2x - 4 equals 2.
To find the value of x, we can use the fact that the sum of the angles in a triangle is 180 degrees. Therefore, we have:
\(x + 2x + 3x = 180\\6x = 180\\x = 30\)
Therefore, the value of x is 30 degrees.
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tan(2 sin^-1 0.4)
Find the Exact value
Answers
Answer:
tan(2u)=[4sqrt(21)]/[17]
Step-by-step explanation:
Let u=arcsin(0.4)
tan(2u)=sin(2u)/cos(2u)
tan(2u)=[2sin(u)cos(u)]/[cos^2(u)-sin^2(u)]
If u=arcsin(0.4), then sin(u)=0.4
By the Pythagorean Identity, cos^2(u)+sin^2(u)=1, we have cos^2(u)=1-sin^2(u)=1-(0.4)^2=1-0.16=0.84.
This also implies cos(u)=sqrt(0.84) since cosine is positive.
Plug in values:
tan(2u)=[2(0.4)(sqrt(0.84)]/[0.84-0.16]
tan(2u)=[2(0.4)(sqrt(0.84)]/[0.68]
tan(2u)=[(0.4)(sqrt(0.84)]/[0.34]
tan(2u)=[(40)(sqrt(0.84)]/[34]
tan(2u)=[(20)(sqrt(0.84)]/[17]
Note:
0.84=0.04(21)
So the principal square root of 0.04 is 0.2
Sqrt(0.84)=0.2sqrt(21).
tan(2u)=[(20)(0.2)(sqrt(21)]/[17]
tan(2u)=[(20)(2)sqrt(21)]/[170]
tan(2u)=[(2)(2)sqrt(21)]/[17]
tan(2u)=[4sqrt(21)]/[17]
you have $20 to spend on a taxi fare. The ride costs $5 plus $2.50 per kilometer.
Answers
Answer:
What is the question?
Step-by-step explanation:
Answer:
Im gonna assume you want to know how far you can get with the entire 20$
Step-by-step explanation:
so its 5$ already and 2kilometers is another 5. SO you can get 6 kilometers with all of your 20$
Zack is on his school's color guard and is practicing throwing and catching his flag. He throws the flag into the air from a height of 5 feet at a velocity of 30 feet per second. After the flag starts to come back down, he catches it 7 feet above the ground.
To the nearest tenth of a second, how long is the flag in the air before Zack catches it?
Hint: Use the formula h=16t2+vt+s.
Answers
The Nearest tenth of a second, the flag is in the air for approximately 0.1 seconds before Zack catches it.
To determine the time the flag is in the air before Zack catches it, we can use the kinematic equation for vertical motion:
h = 16t^2 + vt + s
Where:
h is the height of the flag,
t is the time in seconds,
v is the initial vertical velocity of the flag,
s is the initial height of the flag.
In this case, the flag is thrown into the air from a height of 5 feet (s = 5) with an initial vertical velocity of 30 feet per second (v = 30). Zack catches it at a height of 7 feet (h = 7).
We can rewrite the equation as:
7 = 16t^2 + 30t + 5
To find the time (t) when the flag is at a height of 7 feet, we can rearrange the equation and solve for t. However, since this is a quadratic equation, we can also use the quadratic formula.
The quadratic equation in this case is:
16t^2 + 30t + 5 - 7 = 0
16t^2 + 30t - 2 = 0
Now, we can use the quadratic formula:
t = (-b ± √(b^2 - 4ac)) / (2a)
Applying the values from the quadratic equation, we have:
t = (-30 ± √(30^2 - 4 * 16 * (-2))) / (2 * 16)
Simplifying further:
t = (-30 ± √(900 + 128)) / 32
t = (-30 ± √1028) / 32
Using a calculator, we find two solutions:
t ≈ -1.08 seconds or t ≈ 0.06 seconds
Since time cannot be negative in this context, we discard the negative solution.
Therefore, to the nearest tenth of a second, the flag is in the air for approximately 0.1 seconds before Zack catches it.
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