8.3 Trig Equations - Mrs. Johnstonjohnstonmadison.weebly.com/uploads/5/9/8/1/59818271/8.3... ·...

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Solve Trigonometric Equations in basic form.

Solve Trig Equations by substitution.

Solve Trigonometric Equations by factoring.

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Make sure you are in degree mode

◦ 1) identify the 2 quadrants where the answers fall

◦ 2) type the inverse function into your calculator and get an answer in degrees

◦ 3) use that answer to fill in your two triangles in the identified quadrants

◦ 4) convert both answers into radians

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Ex 2) Solve sin x = -0.75 Ex 3) tan x = 3

Ex 4) 8 cos x – 1 = 0

Ex 5) 3 cos x + 1 = 0

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Some equations are more complicated and require other strategies to solve.

If the equation contains an x with a coefficient, you will need to do substitution and replacement to get the correct answers

If there is a square in the equation, you will need to factor

1) Substitute u for the bx term

2) Solve for u, include all answers

3) Replace the u with bx

4) Solve for x by dividing all the pieces by b

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1) Substitute u for the trig expression

2) Factor the new u expression

3) Set each piece =0 and solve for u

4) Replace the u with the trig function

5) Solve the trig function

Remember each trig function may have multiple answers

Ex 9) 3 sin2 x – sin x – 2 = 0 Ex 10) 4 sin2 x + 5 sin x + 1 = 0