Pre-Calculus/Trig3 Names Answer Key

Answers to Review Chapter 4.1-4.4 Block Date

Sketch the following in standard position.

Determine the quadrant the angle lies in (if it is on an axis, state which axis it is on and if it is + or – axis)

Then determine the reference angle.

1. 2. –95o 3. 4. 660 °

Quadrant I Quadrant III Quadrant IV Quadrant IV

Ref. Angle Ref. Angle 85o Ref. Angle Ref. Angle 60°

Convert the following from degrees to radians. Convert the following from radians to degrees.

5. –224o 6. 750o 7. 8.

225° -480o

Find a positive and negative coterminal angle for each of the following.

9. 225o 10. 11. 12.

13. Find the arc length and the area of the sector given: r = 5cm and = 45o.

s= r q = 5()= cm = 1.25p cm = 3.93cm

A = ½ r2 q = ½ (5)2 () = cm2= 9.82cm2

14. Find the angle of the sector given d = 14mm and s = 27 mm. Then determine the area of the sector.

s = r q A = ½ r2 q

27 = 7 q A = ½ (7)2()

= q A = 94.5 mm2

3.857 = q

Write the (x , y) coordinates of the following angles. Then find the exact value.

15. cos 240o 16. csc 330o 17. sec -2p 18. sin

(1 , 0)

-2 1

Find the values of in both degrees and radians given the following information.

19. sin = 20. tan = 1 21. sec = Æ

45o, 135o, 45o, 225o, 90o, 270o,

The terminal side of the angle contains the following point.

Find the values of the six trigonometric functions for the following points.

22. (4, -4) 23. (0, -7)

sinθ = cscθ = sinθ = -1 cscθ = -1

cosθ = secθ = cosθ = 0 secθ = Æ

tanθ = -1 cotθ = -1 tanθ = Æ cotθ = 0

Given the following, state the six trigonometric ratios.

24. secq = , Quad III 25. tan q = , Quad I

sinθ = cscθ = sinθ = cscθ = 2

cosθ = secθ = cosθ = secθ =

tanθ = cotθ = tanθ = cotθ =

Use a calculator to find each value: (round to 2 decimal places if necessary)

26. sin 81o 27. tan - 135o 28. cos

.9877 1 .1736

.99 .17

29. sec –270o 30. cot 31. cot 90o

= Æ -1 = 0