Trig Frog's Quiz
Take this quiz as thou wouldst an in-class test. Try thy hand at all the problems and then review thine answers by clicking on the "Answers" link on the navigation bar at thy left.
In problems 1 - 3, use the sum and difference formulae to find the exact values.
1. sin75° = sin(45° + 30°)
2. cos135° = cos(90° + 45°)
3. tan195° = tan(225° - 30°)
In problems 4 and 5, use the double angle formulae for the given values.
4. cos2A, A = pi/4
5. tan2A, A = 60°
In problem 6, verify the identity.
6. tan2x = (2tan x)/(1 - tan^2 x)
In problems 7 and 8, rewrite the expression in terms of the first power of cosine.
7. cos^4 x
8. sin^2 x cos^2 x
In problems 9 - 12, use the half-angle formulae for the given values.
9. cos x/2, x = 60°
10. sin x/2, x = pi/2
11. tan x/2, x = 2pi/3
12. cos x/2, x = 420°
In problems 13 - 16, rewrite the product as a sum (or difference) of sines and cosines of positive arguments.
13. sin41°cos24°
14. cos53°cos40°
15. sin3x cos5x
16. cos4x cos7x
In problems 17 - 20, rewrite the sum (or difference) as a product of sines and cosines of positive arguments.
17. cos46° + cos12°
18. sin54° + sin22°
19. sin3x + sin9x
20. cos8x - cos10x
