BackUse the given information to find the quadrant of s + t. See Example 3.
sin s = 3/5 and sin t = -12/13, s in quadrant I and t in quadrant III
Find the exact value of each expression. (Do not use a calculator.)
cos π/12
Express each function as a trigonometric function of x. See Example 5.
cos 4x
In Exercises 69–74, rewrite each expression as a simplified expression containing one term. sin (α - β) cos β + cos (α - β) sin β
Find the exact value of each expression. (Do not use a calculator.)
cos 105° (Hint: 105° = 60° + 45°)
Write each function value in terms of the cofunction of a complementary angle.
sin (2π/5)
In Exercises 57–64, find the exact value of the following under the given conditions:
b. sin (α + β)
sin α = 3/5, α lies in quadrant I, and sin β = 5/13, β lies in quadrant II.
Write each function as an expression involving functions of θ or x alone. See Example 2.
cos(θ - 30°)
In Exercises 35–38, find the exact value of the following under the given conditions:
e. cos(β/2)
sin α = 3/5, 0 < α < 𝝅/2, and sin β = 12/13, 𝝅/2 < β < 𝝅.
Use the given information to find tan(x + y).
sin y = - 2/3, cos x = -1/5, x in quadrant II, y in quadrant III
Use the given information to find sin(x + y), cos(x - y), tan(x + y), and the quadrant of x + y.
sin x = 3/5, cos y = 24/25, x in quadrant I, y in quadrant IV