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Lesson 5 Contents Example 1Use Sum and Difference of Angles Formulas Example 2Use Sum and Difference Formulas to Solve a Problem Example 3Verify Identities

Example 5-1a Find the exact value of sin 75 . Use the formula. Sum of angles Evaluate each expression.

Example 5-1b Multiply. Simplify. Answer:

Example 5-1c Find the exact value of cos (–75  ). Use the formula Difference of angles Evaluate each expression.

Example 5-1d Multiply. Simplify. Answer:

Example 5-1e Find the exact value of each expression. a. sin 105  b. cos (–120  ) Answer:

Example 5-2a Physics On June 22, the maximum amount of light energy falling on a square foot of ground at a location in the northern hemisphere is given by where  is the latitude of the location and E is the amount of light energy when the Sun is directly overhead. Use the difference of angles formula to determine the amount of light energy in Raleigh, North Carolina, located at 35.8  N. Use the difference formula for sine.

Example 5-2b Answer:In Raleigh, North Carolina, the maximum light energy per square foot is E.

Example 5-2c Use the formulaand the difference of angles formula to determine the amount of light energy in Columbus, Ohio, located at 40  N. Answer: E

Example 5-3a Verify that is an identity. Difference of angles formula Evaluate each expression. Simplify. Original equation Answer:

Example 5-3b Verify that is an identity. Simplify. Answer: Original equation Difference of angles formula Evaluate each expression.

Example 5-3c Verify that each of the following is an identity. a. Answer:

Example 5-3d Verify that each of the following is an identity. b. Answer:

End of Lesson 5