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)
 $4\cos^2x+2\cos x-2\sqrt{2}\cos x=\sqrt{2}$  

•  $\frac{4\pi}{3}$  
  

•  $\frac{\pi}{4}$  

•  $\frac{\pi}{3}$  

•  $\frac{7\pi}{4}$  

•  $\frac{2\pi}{3}$