Section 5.4 Sum and Difference Formulas These formulas will be given to you on the test.
Sine Formulas Signs are the same
Signs are opposite Cosine Formulas
Opposite signs Signs are the same Tangent Formulas
Example 1 Find the exact value for sin 75° using a sum or difference formula.
sin 75° =sin (45° + 30°) = sin 45° cos 30° + cos 45° sin 30°
Example 2
Example 3
Example 4 Find the exact value of cos 25° cos 20° − sin 25° sin 20° = cos (25° + 20°) = cos 45°
Example 5 Write sin(arctan 1 + arccos x) as an algebraic expression.
This expression fits the formula sin (u + v). Angles u = arctan 1 and v = arccos x. sin (u + v) = sin u cos v + cos u sin v 1 1 u 1 x v = sin(arctan 1) cos(arccos x) + cos(arctan 1) sin(arccos x)
1 1 u 1 x v sin (u + v) = sin(arctan 1) cos(arccos x) + cos(arctan 1) sin(arccos x)
Example 6 In the interval [0, 2π) find all of the solutions of
Example 7 Verify the identity.