# Solving trig equations

#### Unicornstodope

##### New member
Can’t figure this equation out, can someone help?

sin^2 (5x)=1

#### Unicornstodope

##### New member

2cos^2 (4theta) +3cos(4theta) +1=0

#### MarkFL

##### Super Moderator
Staff member
Can’t figure this equation out, can someone help?

sin^2 (5x)=1
What do you get if you take the square root of both sides?

2cos^2 (4theta) +3cos(4theta) +1=0
Observe that you have a quadratic in $$\cos(4x)$$...can you proceed?

Yes

#### MarkFL

##### Super Moderator
Staff member
For the first one, we get:

$$\displaystyle \sin(5x)=\pm1$$

This implies:

$$\displaystyle 5x=\frac{\pi}{2}+k\pi=\frac{\pi}{2}(2k+1)$$ where $$k\in\mathbb{Z}$$

Hence:

$$\displaystyle x=\frac{\pi}{10}(2k+1)$$

Does this make sense? What do you get when factoring the second equation?

I got this one

#### Unicornstodope

##### New member
Just need the first one please

#### MarkFL

##### Super Moderator
Staff member
I gave a complete solution for the first one, and I am hoping you will show you work on the second.

#### Unicornstodope

##### New member
The 1 first one is different I figured the second one

#### mmm4444bot

##### Super Moderator
Staff member
The [first] one is different[.] I figured the second one[.]
I tried to parse your wording, above. (Your last post is not clear, regarding what you're working on now or what kind of help you need.)

Please follow the forum guidelines (see the Read Before Posting notice). Show what you've started on the exercise you need help with, or explain why you're stuck.

In the future, please start a new thread for each new exercise. Cheers!

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