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5.4 sum and difference formulas - utep
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5.4 sum and difference formulas - utep
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5.4 SUM AND DIFFERENCE FORMULAS. Copyright © Cengage ... Example 5 – Proving a Cofunction identity. Solution: ... Prove the cofunction identity. = sin x.
5.4
SUM AND DIFFERENCE FORMULAS
Copyright © Cengage Learning. All rights reserved.
Using Sum and Difference Formulas
2
Using Sum and Difference Formulas
3
Example 1 – Evaluating a Trigonometric Function Find the exact value of Solution: To find the exact value of
.
, use the fact that
Consequently, the formula for sin(u – v) yields
4
Example 1 – Solution
cont’d
Try checking this result on your calculator. You will find that 0.259. 5
Using Sum and Difference Formulas = sin x.
6
Example 5 – Proving a Cofunction identity Prove the cofunction identity
= sin x.
Solution: Using the formula for cos(u – v), you have
7
Using Sum and Difference Formulas Sum and difference formulas can be used to rewrite expressions such as and
,
where n is an integer
as expressions involving only sin or cos .
The resulting formulas are called reduction formulas.
8
Example 7 – Solving a Trigonometric Equation Find all solutions of in the interval
.
Solution: Using sum and difference formulas, rewrite the equation as
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Example 7 – Solution
So, the only solutions in the interval and
cont’d
are
. 10
More… Find all solutions of the equations in the interval [0,2𝜋)
1. cos(𝑥 −
𝜋 ) 2
+ sin2 𝑥 = 0
2. tan(𝑥 + 𝜋) + 2 sin(𝑥 + 𝜋) = 0 Write the trigonometric expression as an algebraic expression: sin(arctan 2𝑥 − arccos 𝑥)
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