Ch. 3 - Trigonometric Identities and Equations
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- In Exercises 1–60, verify each identity. sin x sec x = tan x
Problem 1
- In Exercises 1–6, use the figures to find the exact value of each trigonometric function.
Problem 1
sin 2θ
- In Exercises 1–6, use the figures to find the exact value of each trigonometric function.
Problem 2
cos 2θ
- In Exercises 1–6, use the figures to find the exact value of each trigonometric function.
Problem 3
tan 2θ
- In Exercises 1–60, verify each identity. tan (-x) cos x = -sin x
Problem 3
- In Exercises 1–6, use the figures to find the exact value of each trigonometric function.
Problem 4
sin 2α
- Use 105° = 135° - 30° to find the exact value of 105°.
Problem 5
- Be sure that you've familiarized yourself with the first set of formulas presented in this section by working C1–C4 in the Concept and Vocabulary Check. In Exercises 1–8, use the appropriate formula to express each product as a sum or difference. sin x cos 2x
Problem 5
- In Exercises 1–60, verify each identity. tan x csc x cos x = 1
Problem 5
- In Exercises 1–6, use the figures to find the exact value of each trigonometric function.
Problem 6
tan 2α
- In Exercises 7–14, use the given information to find the exact value of each of the following: a. sin 2θ 15 sin θ = -------- , θ lies in quadrant II. 17
Problem 7
- In Exercises 7–14, use the given information to find the exact value of each of the following: b. cos 2θ 15 sin θ = -------- , θ lies in quadrant II. 17
Problem 7
- In Exercises 7–14, use the given information to find the exact value of each of the following: c. tan 2θ 15 sin θ = -------- , θ lies in quadrant II. 17
Problem 7
- Be sure that you've familiarized yourself with the first set of formulas presented in this section by working C1–C4 in the Concept and Vocabulary Check. In Exercises 1–8, use the appropriate formula to express each product as a sum or difference. 3x x cos -------- sin ------- 2 2
Problem 7
- In Exercises 7–14, use the given information to find the exact value of each of the following: a. sin 2θ 12 sin θ = -------- , θ lies in quadrant II. 13
Problem 8
- In Exercises 7–14, use the given information to find the exact value of each of the following: b. cos 2θ 12 sin θ = -------- , θ lies in quadrant II. 13
Problem 8
- In Exercises 7–14, use the given information to find the exact value of each of the following: c. tan 2θ 12 sin θ = -------- , θ lies in quadrant II. 13
Problem 8
- In Exercises 7–14, use the given information to find the exact value of each of the following: b. cos 2θ 24 cos θ = -------- , θ lies in quadrant IV. 25
Problem 9
- In Exercises 7–14, use the given information to find the exact value of each of the following: c. tan 2θ 24 cos θ = -------- , θ lies in quadrant IV. 25
Problem 9
- In Exercises 7–14, use the given information to find the exact value of each of the following: a. sin 2θ 24 cos θ = -------- , θ lies in quadrant IV. 25
Problem 9
- In Exercises 7–14, use the given information to find the exact value of each of the following: a. sin 2θ cot θ = 2, θ lies in quadrant III.
Problem 11
- In Exercises 7–14, use the given information to find the exact value of each of the following: b. cos 2θ cot θ = 2, θ lies in quadrant III.
Problem 11
- In Exercises 7–14, use the given information to find the exact value of each of the following: c. tan 2θ cot θ = 2, θ lies in quadrant III.
Problem 11
- In Exercises 1–60, verify each identity. csc θ - sin θ = cot θ cos θ
Problem 11
- In Exercises 7–14, use the given information to find the exact value of each of the following: c. tan 2θ cot θ = 3, θ lies in quadrant III.
Problem 12
- In Exercises 7–14, use the given information to find the exact value of each of the following: a. sin 2θ 2 sin θ = ﹣ -------- , θ lies in quadrant III. 3
Problem 14
- In Exercises 7–14, use the given information to find the exact value of each of the following: b. cos 2θ 2 sin θ = ﹣ -------- , θ lies in quadrant III. 3
Problem 14
- In Exercises 7–14, use the given information to find the exact value of each of the following: c. tan 2θ 2 sin θ = ﹣ -------- , θ lies in quadrant III. 3
Problem 14
- Use one or more of the six sum and difference identities to solve Exercises 13–54. In Exercises 13–24, find the exact value of each expression. sin(60° - 45°)
Problem 14
- In Exercises 1–60, verify each identity. cos θ sec θ ----------------- = tan θ cot θ
Problem 14