University:
Whitman College
Course:
MATH-125 | Calculus I
Academic year:

2020
Views:

423

Pages:

1
Author:

Keenan Fowler

Extra Practice: Trigonometry 1. Evaluate the following (exactly, without a calculator): (a) sin(3π/4) (c) tan(2π/3) (e) csc(29π/6) (b) cos(−5π/4) (d) sec(7π/6) (f) tan(π/4) 2. What is the amplitude, period and frequency for f (x) = 1 + 2 cos(3x) 3. What is the period of f (x) = tan(π/x)? f (x) = cos(x/π)? 4. Solve for x: (a) 2 cos(x) + 1 = 0 (b) 3 cot2 (x) = 1 (c) sin(x) > cos(x) 5. Review the definition of the inverse trigonometric functions, then compute the following, if possible: (a) sin−1 (0) (d) sin−1 (2) (g) tan−1 (1) (b) sin−1 (1) √ (e) tan−1 (− 3) (c) arcsin(1/2) (f) tan−1 (0) = 0 (h) sec−1 (−2) √ (i) sec−1 (2/ 3) 6. Inverse trig identities: Simplify each expression. (a) sin−1 (sin(π)) (c) tan−1 (tan(π/4)) (b) sin(sin−1 (3/5) (d) tan−1 (tan(π)) 7. Simplify the following expressions (using a triangle). Also think about the value(s) of x for which the simplification is valid. (a) tan(sin−1 (x)) (d) tan(sec−1 (x)) (b) cos(tan−1 (x)) (e) (*) cos(2 sin−1 (x)) (c) sec(sin−1 (x)) (f) (**) sin(2 tan−1 (x)) Hints: (*) Use cos(2x) = cos2 x − sin2 x, (**) Use sin(2x) = 2 sin(x) cos(x) 1

Extra Practice Trigonometry

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