Solving Trigonometric Equations

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

 $\cos x\cdot\sin x=3\cos x$  

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

we CAN NOT cancel  $\cos\ x$  in the expression  $\frac{\cos x\ \sin x}{\cos x}=0$  

why?

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

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

• $$\frac{\pi}{2}$$  

• $$\frac{\pi}{4}$$  

• $$\frac{3\pi}{4}$$  

• $$\frac{3\pi}{2}$$  

Poll

$$\cos^4x+\cos^2x-2=0$$  

how will we solve this question

• factoring

• quadratic formula

Multiple Select

check all the solutions to

$$x^2+x-2=0$$  

• 0

• -2

• 2

• 1

Multiple Select

What are the solutions to $$\left(\cos^2x\right)^2+\cos^2x-2=0$$  

• 0

• $$\frac{\pi}{2}$$  

• $$\pi$$  

• 2  $$\pi$$  

Multiple Select

challenge question (check all answers)
$$4\cos^2x+2\cos x-2\sqrt{2}\cos x=\sqrt{2}$$  

• $$\frac{4\pi}{3}$$  
  

• $$\frac{\pi}{4}$$  

• $$\frac{\pi}{3}$$  

• $$\frac{7\pi}{4}$$  

• $$\frac{2\pi}{3}$$