MATH 175: Chapter 7 Review Analytic Trigonometry - The Learning ...

VII. Can You Solve Equations Involving Trigonometric Functions?
A. Solve Equations Involving a Single Trigonometric Function.
37) Solve the equation
2
4sin 1 on the interval 0 ≤ θ < 2π.
38) Solve the equation 5 2 sin 4 1on the interval 0 ≤ θ < 2π.
39) Solve the equation
3
cos(2 )
2
on the interval 0 ≤ θ < 2π.
40) Solve the equation
cos
2
2
. Give a general formula for all the solutions.
41) Use your graphing utility to solve the equation csc θ = -2 on the interval 0 ≤ θ < 2π. Round the
answer to two decimal places.
42) A mass hangs from a spring which oscillates up and down. The position P (in feet) of the mass at
time t (in seconds) is given by P = 4cos(4 t ) . For what values of t, 0 ≤ t < π, will the position be
2 2 feet? Find the exact values. Do not use a calculator.
B. Solve Equations That Are Quadratic in Form.
43) Solve the equation
44) Solve the equation
C. Solve Trigonometric Equations Using Identities.
45) Solve the equation
46) Solve the equation
2
cos 2cos 1 0 on the interval 0 ≤ θ < 2π.
2
2sin 3sin 2 0 on the interval 0 ≤ θ < 2π.
2
sin 5(cos 1) on the interval 0 ≤ θ < 2π.
2
cos(2 ) 6sin 2 on the interval 0 ≤ θ < 2π.
47) Solve the equation sin(2θ) + sin θ = 0 on the interval 0 ≤ θ < 2π.
D. Use a Calculator to Solve Equations That Include Trigonometric Functions.
48) Use your graphing utility to solve the equation 6x - 5 sin x = 2. Round the solution(s) to two
decimal places if necessary.
2
49) Use a graphing utility to solve the equation 11 24sin x 16cos xon the interval
0° ≤ x < 360°. Express the solution(s) rounded to one decimal place.
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