7 Chapter Test

Simplify.

  1. 1. 2 cos2 x-cos x-1cos x-1

  2. 2. (sec xtan x)2-1tan2 x

  3. 3. Rationalize the denominator:

    1-sin θ1+sin θ.

    Assume that the radicand is nonnegative.

  4. 4. Given that x=2 sin θ, express 4-x2 as a trigonometric function without radicals. Assume 0<θ<π/2.

Use the sum or difference identities to evaluate exactly.

  1. 5. sin 75°

  2. 6. tan π12

  3. 7. Assuming that cos u=513 and cos v=1213 and that u and v are between 0 and π/2, evaluate cos (u-v) exactly.

  4. 8. Given that cos θ=-23 and that the terminal side is in quadrant II, find cos (π/2-θ).

  5. 9. Given that sin θ=-45 and θ is in quadrant III, find sin 2θ and the quadrant in which 2θ lies.

  6. 10. Use a half-angle identity to evaluate cos π12 exactly.

  7. 11. Given that sin θ=0.6820 and that ...

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