Solving Trigonometric Equations

solving trigonometric equations

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Poll

What is the zero product property?

• I know and I can explain it

• I heard it before

• never heard of it

Poll

What is factoring?

• I know and i can explain it

• i heard about it

• never heard of it before

Poll

What is the quadratic formula

• I heard about it and can explain it

• i heard about it

• never heard about it

Solving by factoring

• When trigonometric functions cannot be combined on one side of an equation, try factoring and applying the zero product property

• If the equation has quadratic form, factor if possible. If not possible, apply the quadratic Formula

Let's see an example

Multiple Choice

Whats our first step to solve  $$\cos x\sin x=3\cos x$$  

• $$\cos x\sin x-3\cos x=0$$  

• $$\frac{\cos x\sin x}{3\cos x}=0$$  

BE CAREFUL

Multiple Select

$$\cos x\ \sin x-3\cos x=0$$  

Factor and solve (check all possible answers)

• $$\pi$$  

• $$\frac{\pi}{2}$$  

• $$\frac{3\pi}{2}$$  

• 0

• no solution

Multiple Select

you do it! solve and check all possible solutions

$$2\sin x\ \cos x\ =\sqrt{2}\cos\ x$$  

• $$\frac{\pi}{2}$$  

• $$\frac{\pi}{4}$$  

• $$\frac{3\pi}{4}$$  

• $$\frac{3\pi}{2}$$  

Multiple Select

Solve for 0≤x≤2π

2cos²x + cosx = 0

• π/2, 3π/2

• 0, π,2π

• 2π/3, 4π/3

• π/3, 5π/3

Multiple Select

Solve for 0≤x≤2π

4cos²x - 2 = 0

• π/3, 5π/3

• π/4, 7π/4

• 3π/4, 5π/4

• π/6, 11π/6

Multiple Select

Solve for 0≤x≤2π

sinxtanx = sinx

• π/2, 3π/2

• 3π/4, 7π/4

• 0, π, 2π

• π/4, 5π/4

Multiple Choice

Solve for 0≤x≤2π

2sin²x - 5sinx + 2 = 0

• π/6, 5π/6

• 7π/6, 11π/6

• π/3, 2π/3

• 4π/3, 5π/3

Multiple Choice

Solve for 0≤x≤2π

3sin²x + sinx - 4 = 0

• 0, π

• π/2

• π/6, 5π/6

• 3π/2

Multiple Choice

Which of the following is the solution of sin²x + cos²x = 2?

• 0

• π/4

• π/6

• no solution