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Problem 5.30b
Use the given information to find cos(x - y).
sin y = - 2/3, cos x = -1/5, x in quadrant II, y in quadrant III
Problem 5.30c
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
Problem 5.30d
Use the given information to find the quadrant of x + y.
sin y = - 2/3, cos x = -1/5 , x in quadrant II, y in quadrant III
Problem 5.32
If cos x = -0.750 and sin ≈ 0.6614, then tan x/2 ≈ .
Problem 5.32
Use identities to fill in each blank with the appropriate trigonometric function name.
sin 2π/3 = _____ (- π/6)
Problem 5.32
Find the exact value of each expression. See Example 1.
[tan 5π/12 + tan π/4]/[1 - tan 5π/12 tan π/4]
Problem 5.32
Factor each trigonometric expression.
sin³ α + cos³ α
Problem 5.32a
Use the given information to find sin(x + y).
cos x = 2/9, sin y = - 1, x in quadrant IV, y in quadrant III
Problem 5.32b
Use the given information to cos(x - y).
cos x = 2/9, sin y = -1/2, x in quadrant IV, y in quadrant III
Problem 5.32c
Use the given information to find tan(x + y).
cos x = 2/9, sin y = -1/2, x in quadrant IV, y in quadrant III
Problem 5.32d
Use the given information to find the quadrant of x + y.
cos x = 2/9, sin y = -1/2, x in quadrant IV, y in quadrant III
Problem 5.34
Simplify each expression.
√[(1 + cos 76°)/2]
Problem 5.34
Use identities to fill in each blank with the appropriate trigonometric function name.
____ 72° = cot 18°
Problem 5.34
Write each function as an expression involving functions of θ or x alone. See Example 2.
cos(θ - 30°)
Problem 5.34
Each expression simplifies to a constant, a single function, or a power of a function. Use fundamental identities to simplify each expression.
cot α sin α
Problem 5.36
Simplify each expression.
√[(1 + cos 165°)/(1 - cos 165°)]
Problem 5.36
Use identities to fill in each blank with the appropriate trigonometric function name.
tan 24° = 1/ _____ 66°
Problem 5.36
Write each function as an expression involving functions of θ or x alone. See Example 2.
cos(45° - θ)
Problem 5.36
Each expression simplifies to a constant, a single function, or a power of a function. Use fundamental identities to simplify each expression.
cot t tan t
Problem 5.37
Find one value of θ or x that satisfies each of the following.
tan θ = cot(45° + 2θ)
Problem 5.38
Simplify each expression. See Example 4.
2 tan 15°/(1 - tan² 15°)
Problem 5.38
Simplify each expression.
sin 158.2°/(1 + cos 158.2°)
Problem 5.38
Find one value of θ or x that satisfies each of the following.
sin θ = cos(2θ + 30°)
Problem 5.38
Write each function as an expression involving functions of θ or x alone. See Example 2.
sin(45° + θ)
Problem 5.38
Each expression simplifies to a constant, a single function, or a power of a function. Use fundamental identities to simplify each expression.
(csc θ sec θ)/cot θ
Problem 5.39
For each expression in Column I, choose the expression from Column II that completes an identity. One or both expressions may need to be rewritten.
-tan x cos x
Problem 5.39
Simplify each expression.
±√[(1 + cos 18x)/2]
Problem 5.39
Find one value of θ or x that satisfies each of the following.
sec x = csc (2π/3)
Problem 5.40
Find one value of θ or x that satisfies each of the following.
cos x = sin (π/12)
Problem 5.4
Match each expression in Column I with its value in Column II.
cos² (π/6) - sin² (π/6)