# Thread: Solving equations (x4)

1. ## Solving equations (x4)

*As an aside, I'm sorry if my formatting on the equations isn't up to par. If anyone would be willing to tell me how to do it properly- if there is a way-, I'd be glad to learn.

Hi all.~ I've spent my entire day with my nose figuratively jammed into my Pre-Cal book and still can't seem to be able to figure these out; I can't even manage to start them. If anybody could help me at some point tonight that'd be lovely.

**Essentially, I have to find all of the solutions for the equations on the given intervals**

These Three are on the Interval [0, 2pi)
1. 3sin 2x - (3/2) sqrt3 = 0
2. 2sec^2(x/2) - 3sec(x/2) - 2 = 0
3. -sqrt3 cosx + sinx = -sqrt3

This One is on the Interval [-pi, pi]
4. cos2x + 5sinx = -2

A huge thank you to anyone willing to help! This has been killing me.

2. ## Re: Solving equations (x4)

first equation gives us sin 2x = (sqrt 3)/2 and we know that this is the value for sin pi/3
Also the trig ratio sine is positive in 1st and 2nd quadrant thus sin pi/3 = sin 2pi/3 = (sqrt 3 )/2
Hence we have 2x = pi/3 OR 2x= 2pi/3 that gives x = pi/6 or x = pi/3
Similarly proceed for other equations