How Do I Solve Trig Equations with Exact Values in a Given Domain?

[zaddyzad]

Homework Statement

I have two questions sin²x = 1/25 and this obviously becomes sinx= +-(1/5)
I also have cos²-1.5cosx-0.54 and cosx = (-3/10) and (9/5)

Now this is asking for me to solve for the x value in radians in the domain [0,2pi] and I have no idea how to solve these for exact values. Help would be appreciated.

Homework Statement

 

[Mark44]

Homework Statement

I have two questions sin²x = 1/25 and this obviously becomes sinx= +-(1/5)
I also have cos²-1.5cosx-0.54 and cosx = (-3/10) and (9/5)

What does "cos²-1.5cosx-0.54 " mean?
cos(x) can't possibly equal 9/5.

Now this is asking for me to solve for the x value in radians in the domain [0,2pi] and I have no idea how to solve these for exact values. Help would be appreciated.

Homework Statement

 

[zaddyzad]

that was my second equation, and my bad for putting it down as it is an extraneous root.

 

[Mark44]

"cos²-1.5cosx-0.54" is NOT an equation.

Did you mean cos²(x) - 1.5cosx-0.54 = 0?

Are there two separate questions, or do you have a question about a system of two equations?

Help us out here - don't make us guess about this stuff...

 

[zaddyzad]

Sorry, it is two questions. And yes those are my two problems that I need to solve over the domain [0,2pi]
I need help solving for x using inverse trig.

 

[Mark44]

For the first question, if you had sin(x) = ±1/4, there are two numbers in [0, $2\pi$] for which sin(x) = 1/4 and two more in this interval for which sin(x) = -1/4.

If we let θ be the smallest of the four values, we have sin(θ) = 1/4, so θ = sin^-1(1/4). The other value in that interval for which sin(θ) = 1/4 is $\pi - \theta$, or $\pi - sin^{-1}(1/4)$. These are the exact values.

Similar work will get you the two values for which sin(θ) = -1/4.

Your first problem is similar to this.