Solving Trigonometric Equations

Presentation

•

Mathematics

•

10th Grade

•

Hard

Joseph Anderson

FREE Resource

4 Slides • 12 Questions

solving trigonometric equations

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)

$\pi$

$\frac{\pi}{2}$

$\frac{3\pi}{2}$

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?

π/4

π/6

no solution

solving trigonometric equations

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