09:29Formulas for Trigonometric Functions: Sum/Difference, Double/Half-Angle, Prod-to-Sum/Sum-to-ProdProfessor Dave Explains462views2rank
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).134views1rank
Textbook QuestionIn Exercises 1–6, use the figures to find the exact value of each trigonometric function. sin 2θ196views
Textbook QuestionIn Exercises 1–6, use the figures to find the exact value of each trigonometric function. cos 2θ263views
Textbook QuestionIn Exercises 1–6, use the figures to find the exact value of each trigonometric function. tan 2θ185views
Textbook QuestionIn Exercises 1–6, use the figures to find the exact value of each trigonometric function. sin 2α269views
Textbook QuestionFind values of the sine and cosine functions for each angle measure.2x, given tan x = 5/3 and sin x < 0141views
Textbook QuestionMatch each expression in Column I with its value in Column II. 10. cos 67.5°152views
Textbook QuestionFind values of the sine and cosine functions for each angle measure.2θ, given cos θ = (√3)/5 and sin θ > 0181views
Textbook QuestionFind values of the sine and cosine functions for each angle measure.θ, given cos 2θ = 3/4 and θ terminates in quadrant III143views
Textbook QuestionFind values of the sine and cosine functions for each angle measure.θ, given cos 2θ = 2/3 and 90° < θ <180°194views
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.)302views
Textbook QuestionUse the given information to find each of the following.sin x/2 , given cos x = - 5/8, with π/2 < x < π163views
Textbook QuestionDetermine whether the positive or negative square root should be selected.cos 58° = ±√ (1 + cos 116°)/2]154views
Textbook QuestionUse the given information to find each of the following.cos θ/2 , given sin θ = - 4/5 , with 180° < θ < 270°140views
Textbook QuestionUse the given information to find each of the following.cos x/2 , given cot x = -3, with π/2 < x < π148views
Textbook QuestionUse the given information to find each of the following.cot θ/2, given tan θ = -(√5)/2 , with 90° < θ < 180°158views
Textbook QuestionUse the given information to find each of the following.cos θ, given cos 2θ = 1/2 and θ terminates in quadrant II 170views
Textbook QuestionUse the given information to find each of the following.sin x, given cos 2x = 2/3 , with π < x < 3π/2146views
Textbook QuestionMatch each expression in Column I with its value in Column II.cos² (π/6) - sin² (π/6) 135views
Textbook QuestionDetermine whether the positive or negative square root should be selected.sin (-10°) = ± √[(1 - cos (-20°))/2]198views
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 2x178views
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)156views
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 x174views
Textbook QuestionVerify that each equation is an identity.(sin 2x)/(2sin x) = cos² (x/2) - sin² (x/2)156views
Textbook QuestionExpress each function as a trigonometric function of x. See Example 5.cos 3x172views
Textbook QuestionExpress each function as a trigonometric function of x. See Example 5.cos 4x204views
Textbook QuestionVerify that each equation is an identity.cos x = (1 - tan² (x/2))/(1 + tan² (x/2))162views
Textbook QuestionWrite each expression as a sum or difference of trigonometric functions. See Example 7.2 cos 85° sin 140°132views
Textbook QuestionMatch each expression in Column I with its value in Column II.(2 tan (π/3))/(1 - tan² (π/3))127views
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°161views
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°136views
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°164views
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°161views
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°157views
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°162views
Textbook QuestionFind values of the sine and cosine functions for each angle measure.2θ, given cos θ = -12/13 and sin θ > 0135views
Textbook QuestionMatch each expression in Column I with its value in Column II. 8. tan (-π/8)157views
Textbook QuestionIn Exercises 1–6, use the figures to find the exact value of each trigonometric function. tan 2α345views
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. 17185views
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. 17235views
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. 17194views
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. 13217views
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. 13189views
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. 13172views
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. 25178views
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. 25185views
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. 25183views
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.272views
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.307views
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.272views
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.186views
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. 3279views
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. 3187views
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. 3252views
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°268views
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°216views
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 8197views
Textbook QuestionIn Exercises 39–42, use double- and half-angle formulas to find the exact value of each expression. cos² 15° - sin² 15°298views
Textbook QuestionIn Exercises 43–44, express each product as a sum or difference. sin 6x sin 4x214views
Textbook QuestionIn Exercises 43–44, express each product as a sum or difference. sin 7x cos 3x191views
Textbook QuestionIn Exercises 45–46, express each sum or difference as a product. If possible, find this product's exact value. sin 2x - sin 4x192views
Textbook QuestionIn Exercises 47–54, use the figures to find the exact value of each trigonometric function. θ θ 2 sin ------- cos ------- 2 2396views