In one of Grimms Fairy Tales, Rumpelstiltskin has the ability to spin straw into gold

Find the exact values of the six trigonometric functions of if the terminal side of in standard position contains the given point. 1. (-15, 8)

(-3, 0) 3

(4, 4)

Find the exact value of each trigonometric function. 4. sin 300 5

cos 180 6

tan _5 3 7

sec _7 6

Sketch each angle. Then find its reference angle. 8. 235

Sketch each angle. Then find its reference angle.4 2001

Sketch each angle. Then find its reference angle.-240

Suppose is an a ngle in standard position whose terminal side is in the given quadrant. For each function, find the exact values of the remaining five trigonometric functions of . 11. cos _1 2 , Quadrant II 12

cot =- _ 2 2 , Quadrant IV

The maximum height H in feet that a basketball reaches after being shot is given by the formula H
V0 2 (sin
) _ 2 64 , where V0 represents the initial velocity and represents the degree measure of the angle that the path of the basketball makes with the ground. Find the maximum height reached by a ball shot with an initial velocity of 30 feet per second at an angle of 70.

Find the exact values of the six trigonometric functions of if the terminal side of in standard position contains the given point. 14. (7, 24)

(2, 1)

(5, -8)

(4, -3)

(0, -6)

(-1, 0)

2 , - 2

- 3 , 6 F

Find the exact value of each trigonometric function. 22. sin 240

Find the exact value of each trigonometric function.sec 120

Find the exact value of each trigonometric function.tan 300 2

Find the exact value of each trigonometric function.cot 510

Find the exact value of each trigonometric function.csc 5400 2

Find the exact value of each trigonometric function.cos _11 3 2

Find the exact value of each trigonometric function.cot
- _5 6 29.

Find the exact value of each trigonometric function.sin _3 4

Find the exact value of each trigonometric function.sec _3 2 31

Find the exact value of each trigonometric function.csc _17 6 3

Find the exact value of each trigonometric function.cos (-30)

Find the exact value of each trigonometric function.tan
_5 4 S

Sketch each angle. Then find its reference angle. 34. 315

Sketch each angle. Then find its reference angle.240 3

Sketch each angle. Then find its reference angle.5 4 2003

Sketch each angle. Then find its reference angle.5/6/2018

Sketch each angle. Then find its reference angle.-210

Sketch each angle. Then find its reference angle.-125

Sketch each angle. Then find its reference angle.13 7 4

Sketch each angle. Then find its reference angle.-_2 3

Suppose is an angle in standard position whose terminal side is in the given quadrant. For each function, find the exact values of the remaining five trigonometric functions of . 42. cos
_3 5 , Quadrant IV

tan

-_1 5 , Quadrant II

sin
_1 3, Quadrant II

cot

_1 2 , Quadrant III

For Exercises 46 and 47, use the following information. The formula R
V0 2 _ sin 2
32 gives the distance of a baseball that is hit at an initial velocity of V0 feet per second at an angle of
with the ground. 46. If the ball was hit with an initial velocity of 80 feet per second at an angle of 30, how far was it hit?

Which angle will result in the greatest distance? Explain your reasoning.

Anthonys little brother gets on a carousel that is 8 meters in diameter. At the start of the ride, his brother is 3 meters from the fence to the ride. How far will his brother be from the fence after the carousel rotates 240?

Mikhail and Anya visit a local amusement park to ride a skycoaster. After the first several swings, the angle the skycoaster makes with the vertical is modeled by 0.2 cos
t, with measured in radians and t measured in seconds. Determine the measure of the angle for t 0, 0.5, 1, 1.5, 2, 2.5, and 3 in both radians and degrees.

Ships and airplanes measure distance in nautical miles. The formula 1 nautical mile 6077 - 31 cos 2 feet, where is the latitude in degrees, can be used to find the approximate length of a nautical mile at a certain latitude. Find the length of a nautical mile where the latitude is 60. 5

Give an example of an angle for which the sine is negative and the tangent is positive.

Determine whether the following statement is true or false. If true, explain your reasoning. If false, give a counterexample. The values of the secant and tangent functions for any quadrantal angle are undefined.

Use the information on page 776 to explain how you can model the position of riders on a skycoaster.

If the cotangent of angle
is 1, then the tangent of angle
is A -1. C 1. B 0. D 3.

Which angle has a tangent and cosine that are both negative? F 110 H 210 G 180 J 340

Rewrite each degree measure in radians and each radian measure in degrees. (Lesson 13-2) 56. 90

Rewrite each degree measure in radians and each radian measure in degrees.5
3

Rewrite each degree measure in radians and each radian measure in degrees.5

In one of Grimms Fairy Tales, Rumpelstiltskin has the ability to spin straw into gold. Suppose on the first day, he spun 5 pieces of straw into gold, and each day thereafter he spun twice as much. How many pieces of straw would he have spun into gold by the end of the week?

Use Cramers Rule to solve each system of equations.

Use Cramers Rule to solve each system of equations.

Use Cramers Rule to solve each system of equations.

Solve each equation. Round to the nearest tenth. (Lesson 13-1) 63. _a sin 32 = _8 sin

b sin 45 = _21 sin 100

c sin 60 = _3 sin 75