Solve the equation. (Find all solutions of the equation in the interval [0, 2?). Enter your answers as a comma-separated list.) 2 tan(2x) − 2 cot(x) = 0 Use a double-angle formula to rewrite the expression. 5 sin x cos x Use the half-angle formulas to determine the exact values of the sine, cosine, and tangent of the angle. 67° 30'

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.3: The Addition And Subtraction Formulas
Problem 75E
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  1. Solve the equation. (Find all solutions of the equation in the interval [0, 2?). Enter your answers as a comma-separated list.)
    1. 2 tan(2x) − 2 cot(x) = 0
  2. Use a double-angle formula to rewrite the expression.
    1. 5 sin x cos x
  3. Use the half-angle formulas to determine the exact values of the sine, cosine, and tangent of the angle.
    67° 30'
  4. Find all solutions of the equation in the interval [0, 2?). (Enter your answers as a comma-separated list.)
    1. 8 sin x/2+8cos x=0
  5. Use the sum-to-product formulas to find the exact value of the expression.
    1. 7 cos 120° + 7 cos 60°
  6. Solve the equation. (Enter your answers as a comma-separated list. Use n as an integer constant. Enter your response in radians.)
    sin x(sin x + 1) = 0
  7. Find all solutions of the equation in the interval [0, 2?).
    1. 36 sin2 x = 36 − 18 cos x
  8. Find the x-intercepts of the graph. (Enter your answers as a comma-separated list. Use n as an integer constant.)
    1. y = 6 sin ?x + 6 cos ?x
  9. Use inverse functions where needed to find all solutions of the equation in the interval [0, 2?).
    1. tan2 x − 6 tan x − 7 = 0
  10. Solve the equation. (Enter your answers as a comma-separated list. Use n as an integer constant. Enter your response in radians.)
    1. sec2(x) + 6 sec(x) − 16 = 0

Use the given conditions to find the exact values of 

sin(2u),

 

cos(2u),

 and 

tan(2u)

 using the double-angle formulas.

cos(u) = − 
15
17
,     ?/2 < u < ?
 
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