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5.4 - Solving Trig Equations

The CAST rule tells us the sign of the primary trig ratios in all four quadrants.

There are often multiple solutions (two if k = 1, four if k = 2). Ensure you find all solutions that lie in the specified domain.

Steps for Solving Trig Equations

1. Bring most numbers (a and c, NOT k) over to the RHS of the equal sign.

2. Determine the appropriate special triangle and solve for the related acute angle.

3. Determine which quadrants you are solving for.

4. Solve for the two principal angles based on the quadrants.

If k > 1 then continue with the following steps...

5. If k≠1, then multiply the principal angles by . These become your actual principal angles.

6. Next, plug "k" into the period formula and solve for the period.

7. Add the period calculated in step 6 to the two principal angles to solve for the next two principal angles.

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Example OneSolve each equation for

a) sinx=

b)  cosx = 

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c) 2sin2x+1=0

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d)

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Example TwoSolve the equation 2sin2x - 1 = 0 for

Example ThreeRiders of the London Eye (largest Ferris Wheel in Europe) reach a maximum height of 135 m while riding. If riders board the ride 2 m above the ground and the ride takes 30 minutes to complete a single revolution.

a) Develop a function that models the height in metres and time in minutes.

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b) When are riders 101.75 m above the ground?

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Complete: p. 287-289 #1, 3, 7ad, 12, 15, 17, 22.