Evaluating Functions Involving Double Angles In Exercises 21–24, use the given conditions to find the values of sin 2 u , cos 2 u , and tan 2 u using the double-angle formulas. sin u = - 3 5 , 3 π 2 < u < 2 π
Evaluating Functions Involving Double Angles In Exercises 21–24, use the given conditions to find the values of sin 2 u , cos 2 u , and tan 2 u using the double-angle formulas. sin u = - 3 5 , 3 π 2 < u < 2 π
Solution Summary: The author explains that the first category of Trigonometric Identities is functions of multiple angles.
Evaluating Functions Involving Double Angles In Exercises 21–24, use the given conditions to find thevalues of
sin
2
u
,
cos
2
u
, and
tan
2
u
using the double-angle formulas.
identify A, B, C, and D for the sine functions in Exercises 67–70 and sketch their graphs.
Trigonometric Substitution In Exercises 59–62,use the trigonometric substitution to write the algebraicequation as a trigonometric equation of θ, where−π2 < θ < π2. Then find sin θ and cos θ.59. √2 = √4 − x2, x = 2 sin θ60. 2√2 = √16 − 4x2, x = 2 cos θ61. 3 = √36 − x2, x = 6 sin θ62. 5√3 = √100 − x2, x = 10 cos θ
Solving for θ In Exercises 91–96, find two solutions of each equation. Give your answers in degrees (0° ≤ θ < 360°) and in radians (0 ≤ θ < 2π). Do not use a calculator. 91. (a) sin θ = 1 2 92. (a) cos θ = √2 2 (b) sin θ = −1 2 (b) cos θ = −√2 2 93. (a) cos θ = 1 2 94. (a) sin θ = √3 2 (b) sec θ = 2 (b) csc θ = 2√3 3 95. (a) tan θ = 1 96. (a) cot θ = 0 (b) cot θ = −√3 (b) sec θ = −√2
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Fundamental Trigonometric Identities: Reciprocal, Quotient, and Pythagorean Identities; Author: Mathispower4u;https://www.youtube.com/watch?v=OmJ5fxyXrfg;License: Standard YouTube License, CC-BY