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Solving Trigonometric Equations
Section 5.3 Precalculus PreAP/Dual, Revised ยฉ2017 2/4/ :16 PM ยง5.3: Solving Trig Equations
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ยง5.3: Solving Trig Equations
Steps Isolate the trig function. [ex. ๐๐ฌ๐ข๐ง ๐ =๐] Make sure to apply the inverse restrictions, if necessary. I Give all answers [with a +๐๐
๐ or +๐
๐ on all answers] +๐
๐ will come from tan or cot 2/4/ :16 PM ยง5.3: Solving Trig Equations
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ยง5.3: Solving Trig Equations
Example 1 Find all solutions and solve without a calculator for ๐ฌ๐ข๐ง ๐= ๐ ๐ 2/4/ :16 PM ยง5.3: Solving Trig Equations
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ยง5.3: Solving Trig Equations
Example 2 Find all solutions and solve without a calculator for ๐ ๐๐ฌ๐ ๐โ๐=๐ 2/4/ :16 PM ยง5.3: Solving Trig Equations
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ยง5.3: Solving Trig Equations
Example 3 Find all solutions and solve without a calculator for ๐ฌ๐ข๐ง ๐+ ๐ =โ๐ฌ๐ข๐ง ๐ 2/4/ :16 PM ยง5.3: Solving Trig Equations
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ยง5.3: Solving Trig Equations
Example 3 Find all solutions and solve without a calculator for ๐ฌ๐ข๐ง ๐+ ๐ =โ๐ฌ๐ข๐ง ๐ 2/4/ :16 PM ยง5.3: Solving Trig Equations
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ยง5.3: Solving Trig Equations
Your Turn Find all solutions and solve without a calculator for ๐๐จ๐ฌ ๐โ ๐ =โ๐๐จ๐ฌ ๐ 2/4/ :16 PM ยง5.3: Solving Trig Equations
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ยง5.3: Solving Trig Equations
Example 4 Find all solutions and solve without a calculator for ๐ ๐ญ๐๐ง ๐ ๐โ๐=๐ 2/4/ :16 PM ยง5.3: Solving Trig Equations
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ยง5.3: Solving Trig Equations
Example 4 Find all solutions and solve without a calculator for ๐ ๐ญ๐๐ง ๐ ๐โ๐=๐ 2/4/ :16 PM ยง5.3: Solving Trig Equations
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ยง5.3: Solving Trig Equations
Example 5 Find all solutions and solve without a calculator for ๐๐จ๐ญ ๐ ๐๐จ๐ฌ ๐ ๐=๐ ๐๐จ๐ญ ๐ 2/4/ :16 PM ยง5.3: Solving Trig Equations
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ยง5.3: Solving Trig Equations
Example 6 Find all solutions and solve without a calculator for ๐๐๐จ๐ฌ ๐ ๐=๐๐จ๐ฌ ๐ 2/4/ :16 PM ยง5.3: Solving Trig Equations
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ยง5.3: Solving Trig Equations
Your Turn Find all solutions and solve without a calculator for ๐ฌ๐ข๐ง ๐ ๐=๐ ๐ฌ๐ข๐ง ๐ 2/4/ :16 PM ยง5.3: Solving Trig Equations
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๐ผ-Substitution for Trigonometry
Try to get into one trig function As a form of substitution, plug the ๐ in for the variable with trig functions Factor the equation with the substitution Replacing the ๐ back to the original trig function and solve 2/4/ :16 PM ยง5.3: Solving Trig Equations
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ยง5.3: Solving Trig Equations
Example 7 Find all solutions and solve without a calculator for ๐๐ฌ๐ข๐ง ๐ ๐+๐๐๐จ๐ฌ ๐โ๐=๐ 2/4/ :16 PM ยง5.3: Solving Trig Equations
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ยง5.3: Solving Trig Equations
Example 7 Find all solutions and solve without a calculator for ๐๐ฌ๐ข๐ง ๐ ๐+๐๐๐จ๐ฌ ๐โ๐=๐ 2/4/ :16 PM ยง5.3: Solving Trig Equations
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ยง5.3: Solving Trig Equations
Example 7 Find all solutions and solve without a calculator for ๐๐ฌ๐ข๐ง ๐ ๐+๐๐๐จ๐ฌ ๐โ๐=๐ 2/4/ :16 PM ยง5.3: Solving Trig Equations
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ยง5.3: Solving Trig Equations
Example 8 Find all solutions and solve without a calculator for ๐๐จ๐ญ ๐ ๐+๐๐ฌ๐ ๐โ๐=๐ 2/4/ :16 PM ยง5.3: Solving Trig Equations
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ยง5.3: Solving Trig Equations
Your Turn Find all solutions and solve without a calculator for ๐๐ฌ๐๐ ๐ ๐โ๐ ๐ญ๐๐ง ๐ ๐โ๐=๐ 2/4/ :16 PM ยง5.3: Solving Trig Equations
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ยง5.3: Solving Trig Equations
Example 9 Find all solutions and solve without a calculator for ๐ฌ๐ข๐ง ๐๐=โ ๐ ๐ 2/4/ :16 PM ยง5.3: Solving Trig Equations
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ยง5.3: Solving Trig Equations
Example 9 Find all solutions and solve without a calculator for ๐ฌ๐ข๐ง ๐๐=โ ๐ ๐ 2/4/ :16 PM ยง5.3: Solving Trig Equations
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ยง5.3: Solving Trig Equations
Example 10 Find all solutions and solve without a calculator for ๐ ๐๐จ๐ฌ ๐๐โ๐=๐ 2/4/ :16 PM ยง5.3: Solving Trig Equations
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ยง5.3: Solving Trig Equations
Example 11 Find all solutions and solve without a calculator for ๐ ๐ญ๐๐ง ๐ ๐ +๐=๐ from ๐, ๐
2/4/ :16 PM ยง5.3: Solving Trig Equations
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ยง5.3: Solving Trig Equations
Example 11 Find all solutions and solve without a calculator for ๐ ๐ญ๐๐ง ๐ ๐ +๐=๐ from ๐, ๐
2/4/ :16 PM ยง5.3: Solving Trig Equations
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ยง5.3: Solving Trig Equations
Your Turn Find all solutions and solve without a calculator for ๐๐ฌ๐ ๐๐โ ๐ ๐ =๐ 2/4/ :16 PM ยง5.3: Solving Trig Equations
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ยง5.3: Solving Trig Equations
Assignment Page odd, odd, 31 2/4/ :16 PM ยง5.3: Solving Trig Equations
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