Analysis BC - Tredyffrin/Easttown School District



Analysis BC Name: _______________________

Unit 1 Day 5

Trig Functions of Any Angle

1. The point (-24, 10) is on the terminal side of an angle in standard position. Determine the exact values of the six trig functions of the angle.

2. Find the exact values of the six trig functions of θ given csc θ = 4 and cot θ < 0.

3. Find the exact values of the six trig functions of θ given cos θ = -4/5 and θ lies in Quadrant III.

4. Find the exact values of the six trig functions of θ given the terminal side of θ lies on the line 4x + 3y = 0 and lies in Quadrant IV.

5. Give tan θ = 3/2 and that θ lies in Quadrant III, find sec θ.

6. Given csc θ = -2 and that θ lies in Quadrant IV, find cot θ.

7. Given tan θ = -5/4 and θ lies in Quadrant II, find cos(π/2 – θ)

8. Find two solutions for each equation, given 0 ≤ θ < 2π

a. sin θ = ½ b. cos θ = -1/√2 c. cot θ = - √3 d. sec θ = 2

9. Without using a calculator evaluate each of the following

a. sin -240° b. cos 11π/4 c. tan 345π/2 d. sin 32145π

e. sec 34259π/6 f. tan -20π/3 g. sin 3256042π/3

10. You and a friend are standing on two separate cliffs. There is a bison in the valley between the two cliffs. The angle of depression from you to the bison is 23°. The angle of depression from your friend to the bison is 40°. The bison is 45yd from the bottom of your friend’s cliff and two thirds as far from yours. How much taller is your friend’s cliff?

Answers For 1-4 they go cos, sec, sin, csc, tan, cot.

1) -12/13, -13/12, 5/13, 13/5, -5/12, -12/5 2) -√15/4, -4/√15, ¼, 4, -1/√15, -√15

3) -4/5, -5/4, -3/5, -5/3, ¾, 4/3 4) 3/5, 5/3, -4/5, -5/4, -4/3, -3/4

5) -√13/2 6) -√3 7) 5/√41

8) a) π/6, 5π/6 b) 3π/4, 5π/4 c) 5π/6, 11π/6 d) π/3, 5π/3

9) a) √3/2 b) -√2/2 c) undefined d) 0 e) 2/√3 f) √3 g) -√3/2

10) 25.025yd

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