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