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1
Pre-CalculusChapter 5
Analytic Trigonometry
2
5.4 Sum & Difference Formulas
Objectives: Use sum and difference formulas to
evaluate trigonometric functions, verify identities, and solve trigonometric equations.
3
Consider This…. Determine whether each equation is
true or false. Justify your answer.
1cos30cos29cos.2
60sin14sin74sin.1
4
Sum & Difference Formulas Sine
Cosine
Signs are the same.
Signs change.
5
Sum & Difference Formulas Tangent
6
Example 1 Find the exact value of cos 75°.
Check your answer with a calculator.
7
Example 2 Find the exact value of .
12sin
8
Example 3 Simplify.
47tan152tan1
47tan152tan.2
80sin110cos80cos110sin.1
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Example 4 Find the exact value of sin (u + v)
given
where and
where
5
4sin u
20
u
13
12cos v
v2
10
Example 5 Prove the cofunction identity.
xx sin
2cos
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Example 6 Simplify each expression.
3tan.2
2
3cos.1
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Example 7 Find all solutions of the equation in
the interval [0, 2π).
14
sin4
sin
xx
13
Homework 5.4 Worksheet 5.4