6. Trigonometric Identities and More Equations
Double Angle Identities
6. Trigonometric Identities and More Equations
Double Angle Identities - Video Tutorials & Practice Problems
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Double Angle Identities
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Example 1
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Example 2
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Example 3
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Problem
ProblemGiven tanθ=125 and 0 < θ < 2π, find cos(2θ).
A
0
B
−169199
C
169119
D
169144
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PRACTICE PROBLEMS AND ACTIVITIES (83)
- In Exercises 1–6, use the figures to find the exact value of each trigonometric function. sin 2θ
- In Exercises 1–6, use the figures to find the exact value of each trigonometric function. cos 2θ
- In Exercises 1–6, use the figures to find the exact value of each trigonometric function. tan 2θ
- In Exercises 1–6, use the figures to find the exact value of each trigonometric function. sin 2α
- Find values of the sine and cosine functions for each angle measure.2x, given tan x = 5/3 and sin x < 0
- Match each expression in Column I with its value in Column II. 10. cos 67.5°
- Find values of the sine and cosine functions for each angle measure.2θ, given cos θ = (√3)/5 and sin θ > 0
- Use a half-angle identity to find each exact value.sin 195°
- Find values of the sine and cosine functions for each angle measure.θ, given cos 2θ = 3/4 and θ terminates in ...
- Use a half-angle identity to find each exact value.cos 195°
- Find values of the sine and cosine functions for each angle measure.θ, given cos 2θ = 2/3 and 90° < θ <1...
- Use a half-angle identity to find each exact value.sin 165°
- The half-angle identitytan A/2 = ± √[(1 - cosA)/(1 + cos A)]can be used to find tan 22.5° = √(3 - 2√2), and th...
- Use the given information to find each of the following.sin x/2 , given cos x = - 5/8, with π/2 < x < π
- Match each expression in Column I with its value in Column II.(2 tan 15°)/(1 - tan² 15°)
- Determine whether the positive or negative square root should be selected.cos 58° = ±√ (1 + cos 116°)/2]
- Use the given information to find each of the following.cos θ/2 , given sin θ = - 4/5 , with 180° < θ < ...
- Use the given information to find each of the following.cos x/2 , given cot x = -3, with π/2 < x < π
- Use the given information to find each of the following.cot θ/2, given tan θ = -(√5)/2 , with 90° < θ < ...
- Use the given information to find each of the following.cos θ, given cos 2θ = 1/2 and θ terminates in quadra...
- Use the given information to find each of the following.sin x, given cos 2x = 2/3 , with π < x < 3π/2
- If cos x = -0.750 and sin ≈ 0.6614, then tan x/2 ≈ .
- Simplify each expression. √[(1 + cos 76°)/2]
- Simplify each expression. √[(1 + cos 165°)/(1 - cos 165°)]
- Simplify each expression. See Example 4.2 tan 15°/(1 - tan² 15°)
- Simplify each expression.sin 158.2°/(1 + cos 158.2°)
- Simplify each expression.±√[(1 + cos 18x)/2]
- Match each expression in Column I with its value in Column II.cos² (π/6) - sin² (π/6)
- Simplify each expression. See Example 4.1 - 2 sin² 22 ½°
- Determine whether the positive or negative square root should be selected.sin (-10°) = ± √[(1 - cos (-20°))/2]
- Simplify each expression.±√[(1 + cos 20α)/2]
- Simplify each expression.±√[(1 - cos 8θ)/(1 + cos 8θ)]
- Simplify each expression. See Example 4.cos² π/8 - 1/2
- Simplify each expression.±√[(1 - cos 5A)/(1 + cos 5A)]
- Simplify each expression.± √[(1 + cos (x/4))/2]
- Simplify each expression. See Example 4. tan 34°/2(1 - tan² 34°)
- Graph each expression and use the graph to make a conjecture, predicting what might be an identity. Then verif...
- Simplify each expression.±√[(1 - cos (3θ/5))/2]
- Simplify each expression. See Example 4.⅛ sin 29.5° cos 29.5°
- Graph each expression and use the graph to make a conjecture, predicting what might be an identity. Then verif...
- Verify that each equation is an identity.cot² (x/2) = (1 + cos x)²/(sin² x)
- Simplify each expression. See Example 4.cos² 2x - sin² 2x
- Graph each expression and use the graph to make a conjecture, predicting what might be an identity. Then verif...
- Verify that each equation is an identity.(sin 2x)/(2sin x) = cos² (x/2) - sin² (x/2)
- Express each function as a trigonometric function of x. See Example 5.cos 3x
- Verify that each equation is an identity.tan (θ/2) = csc θ - cot θ
- Express each function as a trigonometric function of x. See Example 5.cos 4x
- Verify that each equation is an identity.cos x = (1 - tan² (x/2))/(1 + tan² (x/2))
- Write each expression as a sum or difference of trigonometric functions. See Example 7.2 cos 85° sin 140°
- Match each expression in Column I with its value in Column II.(2 tan (π/3))/(1 - tan² (π/3))
- Advanced methods of trigonometry can be used to find the following exact value.sin 18° = (√5 - 1)/4(See Hobson...
- Advanced methods of trigonometry can be used to find the following exact value.sin 18° = (√5 - 1)/4(See Hobson...
- Advanced methods of trigonometry can be used to find the following exact value.sin 18° = (√5 - 1)/4(See Hobson...
- Advanced methods of trigonometry can be used to find the following exact value.sin 18° = (√5 - 1)/4(See Hobson...
- Advanced methods of trigonometry can be used to find the following exact value.sin 18° = (√5 - 1)/4(See Hobson...
- Advanced methods of trigonometry can be used to find the following exact value.sin 18° = (√5 - 1)/4(See Hobson...
- Find values of the sine and cosine functions for each angle measure.2θ, given cos θ = -12/13 and sin θ > 0
- Match each expression in Column I with its value in Column II. 8. tan (-π/8)
- In Exercises 1–6, use the figures to find the exact value of each trigonometric function. tan 2α
- In Exercises 7–14, use the given information to find the exact value of each of the following: c. tan 2θ 15 ...
- In Exercises 7–14, use the given information to find the exact value of each of the following: b. cos 2θ 15 ...
- In Exercises 7–14, use the given information to find the exact value of each of the following: a. sin 2θ 15 ...
- In Exercises 7–14, use the given information to find the exact value of each of the following: b. cos 2θ 12 ...
- In Exercises 7–14, use the given information to find the exact value of each of the following: a. sin 2θ 12 ...
- In Exercises 7–14, use the given information to find the exact value of each of the following: c. tan 2θ ...
- In Exercises 7–14, use the given information to find the exact value of each of the following: c. tan 2θ 24 ...
- In Exercises 7–14, use the given information to find the exact value of each of the following: b. cos 2θ 24 ...
- In Exercises 7–14, use the given information to find the exact value of each of the following: a. sin 2θ ...
- In Exercises 7–14, use the given information to find the exact value of each of the following: c. tan 2θ co...
- In Exercises 7–14, use the given information to find the exact value of each of the following: b. cos 2θ co...
- In Exercises 7–14, use the given information to find the exact value of each of the following: a. sin 2θ co...
- In Exercises 7–14, use the given information to find the exact value of each of the following: c. tan 2θ co...
- In Exercises 7–14, use the given information to find the exact value of each of the following: c. tan 2θ 2 s...
- In Exercises 7–14, use the given information to find the exact value of each of the following: b. cos 2θ 2 s...
- In Exercises 7–14, use the given information to find the exact value of each of the following: a. sin 2θ 2 s...
- In Exercises 15–22, write each expression as the sine, cosine, or tangent of a double angle. Then find the exa...
- In Exercises 15–22, write each expression as the sine, cosine, or tangent of a double angle. Then find the exa...
- In Exercises 15–22, write each expression as the sine, cosine, or tangent of a double angle. Then find the exa...
- In Exercises 39–42, use double- and half-angle formulas to find the exact value of each expression. cos² 15° ...
- In Exercises 43–44, express each product as a sum or difference. sin 6x sin 4x
- In Exercises 43–44, express each product as a sum or difference. sin 7x cos 3x
- In Exercises 45–46, express each sum or difference as a product. If possible, find this product's exact value....
- In Exercises 47–54, use the figures to find the exact value of each trigonometric function. θ θ 2 sin -----...