How do we solve linear trigometric equations?

         Don't we all wish we can go back to the days where all we had to solve was 2x+7=14? Good and bad news. Good being we get to go back to these kinds of problems

Now the bad news is that it involves trig. Don't be scared yet, its the same basics as solving a regular linear equation. These problems tend to look like: Sin(∅)+2=3. 

    The first step to solving this is to get sin alone. So we subtract two from both sides. Once two is subtracted you are left with: sin(∅)=1. This is where our handy dandy unit circle comes into play. We look to see at what angle sin equals 1 which only happens at 90° this means our answer is 90°. 

      Like everything in math, these problems can get a lot more complex and can have multiple answers. For example if after you've simplified your answer is cos(∅)=√2/2 then you are looking for every where that cosine = √2/2. In this case that would be both at 45° and 315°.

     These problems aren't that hard to figure out, with a little practice you will know where every single angle is, no problem! 

How do we slove reference angle problems?/How to convert between radians & degrees.

     When solving for reference angles its always best to use your unit circle. Your reference angle is between 0 and 90 degrees and you're trying to find the quickest way back to the x-axis. 

      Solving a reference angle problem can be very tricky the best way is to subtract 360° from the angle given. For example if you are given 345° and are asked to find the reference angle you do 345 - 360 and get -15. You take away the negative sign and your reference angle is 15°. Your reference angle is never negative and never more than 90°. 

      Sometimes you maybe asked to solve a reference angle in radians, which looks like 18π/3. The easiest way to solve these are to convert to degrees, solve, and then convert your answer back into radians. To convert to degree you simply divide and multiply times 180. Then to convert back you DIVIDE by 180, simplify, and add π. There's nothing to it!

Why is the Title Pythagorean Identify Appropriate?

Pythagorean Identity is an appropriate title for many reasons. Sine and Cosine are the root of all identies and all others come from these two. When defining 'identity' it can be defined as, an equation that is true no matter what values are chosen. The original Pythagorean Identity is sin^2 θ + cos^2 θ = 1. In the unit circle the hypotenuse is always 1 and the x and y. values are cosine and sine. If you look at the Pythagorean Therom (a^2 + b^2 = c^2) you can see that compared to the Pythagorean Identity it is basically the same thing. Because C is the hypotenuse in the Identity it becomes 1. And cosine and sine are just a and b. Because these two are so related that is why the Pythagorean Identity is an appropriate title. No matter what values you chose it will always be true.