LT 15 Solving Trig Equations

Solve equation for  $0\le\theta<2\pi$  .
 $3\sin^2\theta+4=5+\sin^2\theta$  

•  $\theta=\frac{\pi}{4},\frac{5\pi}{4},\frac{7\pi}{4}$  

•  $\theta=\frac{\pi}{4},\frac{7\pi}{4}$  

•  $\theta=\frac{\pi}{4},\frac{3\pi}{4}$  

•  $\theta=\frac{\pi}{4},\frac{3\pi}{4},\frac{5\pi}{4},\frac{7\pi}{4}$  

Tags

CCSS.HSA.REI.B.4

CCSS.HSF.TF.B.7

Solve for x:
 $\cos2x=0\ \ solve\ for\ the\ interval\ 0\degree\le x\le360\degree$  

•  $45\degree,\ 225\degree$  

•  $135\degree,\ 315\degree$  

•  $45\degree,\ 135\degree,\ 225\degree,\ 315\degree$  

• no solution

 $\tan\ x\ +\ \sqrt{3}=0$   $Solve\ for\ ALL\ values\ in\ terms\ of\ \pi$  

•  $x\ =\ \frac{2\pi}{3}+\pi n$  

•  $x=\frac{2\pi}{3}+2\pi n$  

•  $x=\frac{\pi}{3}+\pi n$  

•  $x=\frac{\pi}{3}+2\pi n$  

Solve for all values of x over the interval  $0\le x\le2\pi$  

• $\frac{3π}{4}and\ \frac{5π}{4}\$

• $\frac{π}{4}and\ \frac{3π}{4}$

• $\frac{π}{4},\frac{3π}{4},\frac{5π}{4}\ and\ \frac{7π}{4}$

• $\frac{\pi}{6}\ and\ \frac{5\pi}{6}$

Solve for all values of x over the interval  $0\le x\le2\pi$  

• $\frac{\pi}{2}$

•  $\frac{\pi}{2}\ and\ \ \pi$ 

• DNE

• $\pi$

 $2\sin x-1=0$   $Solve\ for\ ALL\ values\ in\ terms\ of\ \pi$  

•  $x=\frac{\pi}{6}+2\pi n,\ \ \ \ x=\frac{5\pi}{6}+2\pi n$  

•  $x=\frac{\pi}{3}+\pi n,\ \ \ \ \ x\ =\ \frac{2\pi}{3}+\pi n$  

•  $x=\frac{\pi}{6}+2\pi n,\ \ \ \ \ x=\frac{7\pi}{6}+2\pi n$  

• No Solution

To solve this equation, cos²x + sinx = 1, replace cos²x with

• 1/(sec²x)

• sin²x − 1

• 1 − sin²x

• 1 + tan²x

Organize this equation so it can be factored:

1−sin²x + sinx = 1

• move all to the right: 0 = sin²x − sinx

• cancel the ones and cancel a sinx

• replace sin²x with 1 − cos²x

• use this: 0 = sin²x − sinx + 2

Factor 0 = sin²x − sinx

• 0 = sinx(sinx)

• 0 = sinx(1 − sinx)

• 0 = cosx(sinx − 1)

• 0 = sinx(sinx − 1)

On the domain  $0\le x\le2\pi$   solve this equation 0 = sinx(sinx − 1)

•  $0\pi,\ \pi$  

•  $0\pi,\ \pi,\ \frac{\pi}{2}$  

•  $\frac{\pi}{2}$  

•  $0\pi,\ \frac{\pi}{2}$