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Solving Trigonometric Equations

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Presentation on theme: "Solving Trigonometric Equations"โ€” Presentation transcript:

1 Solving Trigonometric Equations
Section 5.3 Precalculus PreAP/Dual, Revised ยฉ2017 2/4/ :16 PM ยง5.3: Solving Trig Equations

2 ยง5.3: Solving Trig Equations
Steps Isolate the trig function. [ex. ๐Ÿ๐ฌ๐ข๐ง ๐’™ =๐Ÿ] Make sure to apply the inverse restrictions, if necessary. I Give all answers [with a +๐Ÿ๐…๐’ or +๐…๐’ on all answers] +๐…๐’ will come from tan or cot 2/4/ :16 PM ยง5.3: Solving Trig Equations

3 ยง5.3: Solving Trig Equations
Example 1 Find all solutions and solve without a calculator for ๐ฌ๐ข๐ง ๐’™= ๐Ÿ ๐Ÿ 2/4/ :16 PM ยง5.3: Solving Trig Equations

4 ยง5.3: Solving Trig Equations
Example 2 Find all solutions and solve without a calculator for ๐Ÿ‘ ๐œ๐ฌ๐œ ๐’™โˆ’๐Ÿ=๐ŸŽ 2/4/ :16 PM ยง5.3: Solving Trig Equations

5 ยง5.3: Solving Trig Equations
Example 3 Find all solutions and solve without a calculator for ๐ฌ๐ข๐ง ๐’™+ ๐Ÿ =โˆ’๐ฌ๐ข๐ง ๐’™ 2/4/ :16 PM ยง5.3: Solving Trig Equations

6 ยง5.3: Solving Trig Equations
Example 3 Find all solutions and solve without a calculator for ๐ฌ๐ข๐ง ๐’™+ ๐Ÿ =โˆ’๐ฌ๐ข๐ง ๐’™ 2/4/ :16 PM ยง5.3: Solving Trig Equations

7 ยง5.3: Solving Trig Equations
Your Turn Find all solutions and solve without a calculator for ๐œ๐จ๐ฌ ๐’™โˆ’ ๐Ÿ‘ =โˆ’๐œ๐จ๐ฌ ๐’™ 2/4/ :16 PM ยง5.3: Solving Trig Equations

8 ยง5.3: Solving Trig Equations
Example 4 Find all solutions and solve without a calculator for ๐Ÿ‘ ๐ญ๐š๐ง ๐Ÿ ๐’™โˆ’๐Ÿ=๐ŸŽ 2/4/ :16 PM ยง5.3: Solving Trig Equations

9 ยง5.3: Solving Trig Equations
Example 4 Find all solutions and solve without a calculator for ๐Ÿ‘ ๐ญ๐š๐ง ๐Ÿ ๐’™โˆ’๐Ÿ=๐ŸŽ 2/4/ :16 PM ยง5.3: Solving Trig Equations

10 ยง5.3: Solving Trig Equations
Example 5 Find all solutions and solve without a calculator for ๐œ๐จ๐ญ ๐’™ ๐œ๐จ๐ฌ ๐Ÿ ๐’™=๐Ÿ ๐œ๐จ๐ญ ๐’™ 2/4/ :16 PM ยง5.3: Solving Trig Equations

11 ยง5.3: Solving Trig Equations
Example 6 Find all solutions and solve without a calculator for ๐Ÿ๐œ๐จ๐ฌ ๐Ÿ ๐’™=๐œ๐จ๐ฌ ๐’™ 2/4/ :16 PM ยง5.3: Solving Trig Equations

12 ยง5.3: Solving Trig Equations
Your Turn Find all solutions and solve without a calculator for ๐ฌ๐ข๐ง ๐Ÿ ๐’™=๐Ÿ ๐ฌ๐ข๐ง ๐’™ 2/4/ :16 PM ยง5.3: Solving Trig Equations

13 ๐‘ผ-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

14 ยง5.3: Solving Trig Equations
Example 7 Find all solutions and solve without a calculator for ๐Ÿ๐ฌ๐ข๐ง ๐Ÿ ๐’™+๐Ÿ‘๐œ๐จ๐ฌ ๐’™โˆ’๐Ÿ‘=๐ŸŽ 2/4/ :16 PM ยง5.3: Solving Trig Equations

15 ยง5.3: Solving Trig Equations
Example 7 Find all solutions and solve without a calculator for ๐Ÿ๐ฌ๐ข๐ง ๐Ÿ ๐’™+๐Ÿ‘๐œ๐จ๐ฌ ๐’™โˆ’๐Ÿ‘=๐ŸŽ 2/4/ :16 PM ยง5.3: Solving Trig Equations

16 ยง5.3: Solving Trig Equations
Example 7 Find all solutions and solve without a calculator for ๐Ÿ๐ฌ๐ข๐ง ๐Ÿ ๐’™+๐Ÿ‘๐œ๐จ๐ฌ ๐’™โˆ’๐Ÿ‘=๐ŸŽ 2/4/ :16 PM ยง5.3: Solving Trig Equations

17 ยง5.3: Solving Trig Equations
Example 8 Find all solutions and solve without a calculator for ๐œ๐จ๐ญ ๐Ÿ ๐’™+๐œ๐ฌ๐œ ๐’™โˆ’๐Ÿ“=๐ŸŽ 2/4/ :16 PM ยง5.3: Solving Trig Equations

18 ยง5.3: Solving Trig Equations
Your Turn Find all solutions and solve without a calculator for ๐Ÿ‘๐ฌ๐ž๐œ ๐Ÿ ๐’™โˆ’๐Ÿ ๐ญ๐š๐ง ๐Ÿ ๐’™โˆ’๐Ÿ’=๐ŸŽ 2/4/ :16 PM ยง5.3: Solving Trig Equations

19 ยง5.3: Solving Trig Equations
Example 9 Find all solutions and solve without a calculator for ๐ฌ๐ข๐ง ๐Ÿ๐’™=โˆ’ ๐Ÿ ๐Ÿ 2/4/ :16 PM ยง5.3: Solving Trig Equations

20 ยง5.3: Solving Trig Equations
Example 9 Find all solutions and solve without a calculator for ๐ฌ๐ข๐ง ๐Ÿ๐’™=โˆ’ ๐Ÿ ๐Ÿ 2/4/ :16 PM ยง5.3: Solving Trig Equations

21 ยง5.3: Solving Trig Equations
Example 10 Find all solutions and solve without a calculator for ๐Ÿ ๐œ๐จ๐ฌ ๐Ÿ‘๐’•โˆ’๐Ÿ=๐ŸŽ 2/4/ :16 PM ยง5.3: Solving Trig Equations

22 ยง5.3: Solving Trig Equations
Example 11 Find all solutions and solve without a calculator for ๐Ÿ‘ ๐ญ๐š๐ง ๐’™ ๐Ÿ +๐Ÿ‘=๐ŸŽ from ๐ŸŽ, ๐… 2/4/ :16 PM ยง5.3: Solving Trig Equations

23 ยง5.3: Solving Trig Equations
Example 11 Find all solutions and solve without a calculator for ๐Ÿ‘ ๐ญ๐š๐ง ๐’™ ๐Ÿ +๐Ÿ‘=๐ŸŽ from ๐ŸŽ, ๐… 2/4/ :16 PM ยง5.3: Solving Trig Equations

24 ยง5.3: Solving Trig Equations
Your Turn Find all solutions and solve without a calculator for ๐œ๐ฌ๐œ ๐Ÿ๐’™โˆ’ ๐Ÿ ๐Ÿ‘ =๐ŸŽ 2/4/ :16 PM ยง5.3: Solving Trig Equations

25 ยง5.3: Solving Trig Equations
Assignment Page odd, odd, 31 2/4/ :16 PM ยง5.3: Solving Trig Equations


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