09:29Formulas for Trigonometric Functions: Sum/Difference, Double/Half-Angle, Prod-to-Sum/Sum-to-ProdProfessor Dave Explains398views2rank
Multiple ChoiceGiven tanθ=512\tan\theta=\frac{5}{12}tanθ=125 and 0 < θ\thetaθ < π2\frac{\pi}{2}2π, find cos(2θ)\cos\left(2\theta\right)cos(2θ).99views1rank
Textbook QuestionIn Exercises 1–6, use the figures to find the exact value of each trigonometric function. sin 2θ168views
Textbook QuestionIn Exercises 1–6, use the figures to find the exact value of each trigonometric function. cos 2θ210views
Textbook QuestionIn Exercises 1–6, use the figures to find the exact value of each trigonometric function. tan 2θ164views
Textbook QuestionIn Exercises 1–6, use the figures to find the exact value of each trigonometric function. sin 2α231views
Textbook QuestionFind values of the sine and cosine functions for each angle measure.2x, given tan x = 5/3 and sin x < 0103views
Textbook QuestionFind values of the sine and cosine functions for each angle measure.2θ, given cos θ = (√3)/5 and sin θ > 0137views
Textbook QuestionFind values of the sine and cosine functions for each angle measure.θ, given cos 2θ = 3/4 and θ terminates in quadrant III113views
Textbook QuestionFind values of the sine and cosine functions for each angle measure.θ, given cos 2θ = 2/3 and 90° < θ <180°139views
Textbook QuestionThe half-angle identitytan A/2 = ± √[(1 - cosA)/(1 + cos A)]can be used to find tan 22.5° = √(3 - 2√2), and the half-angle identitytan A/2 = sin A/(1 + cos A)can be used to find tan 22.5° = √2 - 1. Show that these answers are the same, without using a calculator. (Hint: If a > 0 and b > 0 and a² = b², then a = b.)181views
Textbook QuestionUse the given information to find each of the following.sin x/2 , given cos x = - 5/8, with π/2 < x < π110views
Textbook QuestionDetermine whether the positive or negative square root should be selected.cos 58° = ±√ (1 + cos 116°)/2]97views
Textbook QuestionUse the given information to find each of the following.cos θ/2 , given sin θ = - 4/5 , with 180° < θ < 270°92views
Textbook QuestionUse the given information to find each of the following.cos x/2 , given cot x = -3, with π/2 < x < π100views
Textbook QuestionUse the given information to find each of the following.cot θ/2, given tan θ = -(√5)/2 , with 90° < θ < 180°102views
Textbook QuestionUse the given information to find each of the following.cos θ, given cos 2θ = 1/2 and θ terminates in quadrant II 109views
Textbook QuestionUse the given information to find each of the following.sin x, given cos 2x = 2/3 , with π < x < 3π/296views
Textbook QuestionMatch each expression in Column I with its value in Column II.cos² (π/6) - sin² (π/6) 103views
Textbook QuestionDetermine whether the positive or negative square root should be selected.sin (-10°) = ± √[(1 - cos (-20°))/2]134views
Textbook QuestionGraph each expression and use the graph to make a conjecture, predicting what might be an identity. Then verify your conjecture algebraically.(1 - cos 2x)/sin 2x116views
Textbook QuestionGraph each expression and use the graph to make a conjecture, predicting what might be an identity. Then verify your conjecture algebraically.(cos x sin 2x)/1 + cos 2x)105views
Textbook QuestionGraph each expression and use the graph to make a conjecture, predicting what might be an identity. Then verify your conjecture algebraically.csc x - cot x107views
Textbook QuestionVerify that each equation is an identity.(sin 2x)/(2sin x) = cos² (x/2) - sin² (x/2)101views
Textbook QuestionExpress each function as a trigonometric function of x. See Example 5.cos 3x120views
Textbook QuestionExpress each function as a trigonometric function of x. See Example 5.cos 4x148views
Textbook QuestionVerify that each equation is an identity.cos x = (1 - tan² (x/2))/(1 + tan² (x/2))106views
Textbook QuestionWrite each expression as a sum or difference of trigonometric functions. See Example 7.2 cos 85° sin 140°106views
Textbook QuestionMatch each expression in Column I with its value in Column II.(2 tan (π/3))/(1 - tan² (π/3))102views
Textbook QuestionAdvanced methods of trigonometry can be used to find the following exact value.sin 18° = (√5 - 1)/4(See Hobson's A Treatise on Plane Trigonometry.) Use this value and identities to find each exact value. Support answers with calculator approximations if desired.cos 18°99views
Textbook QuestionAdvanced methods of trigonometry can be used to find the following exact value.sin 18° = (√5 - 1)/4(See Hobson's A Treatise on Plane Trigonometry.) Use this value and identities to find each exact value. Support answers with calculator approximations if desired.cot 18°90views
Textbook QuestionAdvanced methods of trigonometry can be used to find the following exact value.sin 18° = (√5 - 1)/4(See Hobson's A Treatise on Plane Trigonometry.) Use this value and identities to find each exact value. Support answers with calculator approximations if desired.csc 18°115views
Textbook QuestionAdvanced methods of trigonometry can be used to find the following exact value.sin 18° = (√5 - 1)/4(See Hobson's A Treatise on Plane Trigonometry.) Use this value and identities to find each exact value. Support answers with calculator approximations if desired.tan 72°113views
Textbook QuestionAdvanced methods of trigonometry can be used to find the following exact value.sin 18° = (√5 - 1)/4(See Hobson's A Treatise on Plane Trigonometry.) Use this value and identities to find each exact value. Support answers with calculator approximations if desired.csc 72°105views
Textbook QuestionAdvanced methods of trigonometry can be used to find the following exact value.sin 18° = (√5 - 1)/4(See Hobson's A Treatise on Plane Trigonometry.) Use this value and identities to find each exact value. Support answers with calculator approximations if desired.sin 162°108views
Textbook QuestionFind values of the sine and cosine functions for each angle measure.2θ, given cos θ = -12/13 and sin θ > 0109views
Textbook QuestionMatch each expression in Column I with its value in Column II. 8. tan (-π/8)104views
Textbook QuestionIn Exercises 1–6, use the figures to find the exact value of each trigonometric function. tan 2α287views
Textbook QuestionIn 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. 17159views
Textbook QuestionIn 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. 17190views
Textbook QuestionIn 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. 17159views
Textbook QuestionIn 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. 13191views
Textbook QuestionIn 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. 13156views
Textbook QuestionIn 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. 13135views
Textbook QuestionIn 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. 25154views
Textbook QuestionIn 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. 25153views
Textbook QuestionIn 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. 25146views
Textbook QuestionIn 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.239views
Textbook QuestionIn 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.280views
Textbook QuestionIn 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.223views
Textbook QuestionIn 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.158views
Textbook QuestionIn 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. 3239views
Textbook QuestionIn 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. 3162views
Textbook QuestionIn 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. 3215views
Textbook QuestionIn Exercises 15–22, write each expression as the sine, cosine, or tangent of a double angle. Then find the exact value of the expression. 2 sin 15° cos 15°233views
Textbook QuestionIn Exercises 15–22, write each expression as the sine, cosine, or tangent of a double angle. Then find the exact value of the expression. cos² 105° - sin² 105°177views
Textbook QuestionIn Exercises 15–22, write each expression as the sine, cosine, or tangent of a double angle. Then find the exact value of the expression. 𝝅 2 cos² ------ ﹣ 1 8168views
Textbook QuestionIn Exercises 39–42, use double- and half-angle formulas to find the exact value of each expression. cos² 15° - sin² 15°223views
Textbook QuestionIn Exercises 43–44, express each product as a sum or difference. sin 6x sin 4x188views
Textbook QuestionIn Exercises 43–44, express each product as a sum or difference. sin 7x cos 3x157views
Textbook QuestionIn Exercises 45–46, express each sum or difference as a product. If possible, find this product's exact value. sin 2x - sin 4x166views
Textbook QuestionIn Exercises 47–54, use the figures to find the exact value of each trigonometric function. θ θ 2 sin ------- cos ------- 2 2330views