Trigonometry · Chapter 6 of 11

Compound & multiple angles

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The cosine of a sum or difference of two angles is found using $cos (A \pm B) = cos A cos B \mp sin A sin B$ . These identities let you evaluate trigonometric functions for angles built from standard angles such as $3 0^{\circ}$ , $4 5^{\circ}$ , and $6 0^{\circ}$ . Repeated use of the sum formulas also produces multiple-angle formulas, such as $cos 3 θ = 4 cos^{3} θ - 3 cos θ$ .

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#	Title	Difficulty	Tags
74	The triple angle	Medium	Angle additionDouble angle

From open sources

274

Showing everything, including problems with no answer to check, a missing figure, or a near-copy elsewhere. Show only complete problems

#	Title	Difficulty
103864	Finding the Exact Value Using the Formula for the Cosine of the Difference of Two Angles	Easy
103866	Finding the Exact Value Using the Formula for the Sum of Two Angles for Cosine	Easy
103868	Using Sum and Difference Identities to Evaluate the Difference of Angles	Easy
103869	Finding the Exact Value of an Expression Involving an Inverse Trigonometric Function	Easy
103870	Finding the Exact Value of an Expression Involving Tangent	Easy
103873	Finding a Cofunction with the Same Value as the Given Expression	Easy
103875	Verifying an Identity Involving Sine	Easy
103876	Verifying an Identity Involving Tangent	Easy
103877	Sum and Difference Identities · Try It 5	Easy
103878	Sum and Difference Identities · Exercise 1	Easy
103880	Sum and Difference Identities · Exercise 3	Easy
103898	Sum and Difference Identities · Exercise 21	Medium
103912	Sum and Difference Identities · Exercise 35	Medium
103916	Sum and Difference Identities · Exercise 39	Medium
103918	Sum and Difference Identities · Exercise 41	Medium
103920	Sum and Difference Identities · Exercise 43	Medium
103924	Sum and Difference Identities · Exercise 47	Deep
103926	Sum and Difference Identities · Exercise 49	Deep
103928	Sum and Difference Identities · Exercise 51	Deep
103931	Sum and Difference Identities · Exercise 55	Deep
103935	Using the Double-Angle Formula for Cosine without Exact Values	Easy
103936	Using the Double-Angle Formulas to Verify an Identity	Easy
103937	Double-Angle, Half-Angle, and Reduction Formulas · Try It 2	Easy
103938	Verifying a Double-Angle Identity for Tangent	Easy
103939	Double-Angle, Half-Angle, and Reduction Formulas · Try It 3	Easy
103940	Writing an Equivalent Expression Not Containing Powers Greater Than 1	Easy
103941	Using the Power-Reducing Formulas to Prove an Identity	Easy
103942	Double-Angle, Half-Angle, and Reduction Formulas · Try It 4	Easy
103943	Using a Half-Angle Formula to Find the Exact Value of a Sine Function	Easy
103947	Double-Angle, Half-Angle, and Reduction Formulas · Exercise 1	Easy
103949	Double-Angle, Half-Angle, and Reduction Formulas · Exercise 3	Easy
103951	Double-Angle, Half-Angle, and Reduction Formulas · Exercise 5	Medium
103955	Double-Angle, Half-Angle, and Reduction Formulas · Exercise 9	Medium
103967	Double-Angle, Half-Angle, and Reduction Formulas · Exercise 21	Medium
103969	Double-Angle, Half-Angle, and Reduction Formulas · Exercise 23	Medium
103973	Double-Angle, Half-Angle, and Reduction Formulas · Exercise 27	Medium
103981	Double-Angle, Half-Angle, and Reduction Formulas · Exercise 35	Medium
103983	Double-Angle, Half-Angle, and Reduction Formulas · Exercise 37	Medium
103987	Double-Angle, Half-Angle, and Reduction Formulas · Exercise 41	Medium
103989	Double-Angle, Half-Angle, and Reduction Formulas · Exercise 43	Medium
103991	Double-Angle, Half-Angle, and Reduction Formulas · Exercise 45	Medium
103995	Double-Angle, Half-Angle, and Reduction Formulas · Exercise 49	Medium
104001	Double-Angle, Half-Angle, and Reduction Formulas · Exercise 55	Deep
104003	Double-Angle, Half-Angle, and Reduction Formulas · Exercise 57	Deep
104005	Double-Angle, Half-Angle, and Reduction Formulas · Exercise 59	Deep
104007	Double-Angle, Half-Angle, and Reduction Formulas · Exercise 61	Deep
104009	Double-Angle, Half-Angle, and Reduction Formulas · Exercise 63	Deep
104010	Writing the Product as a Sum Using the Product-to-Sum Formula for Cosine	Easy
104012	Writing the Product as a Sum Containing only Sine or Cosine	Easy
104014	Express the Product as a Sum or Difference	Easy