Solving Trigonometric Equations Part 1

        Hi Pre Calc. class! Last time you guys learned about the unit circle, and all of it's properties, special angles, etc. Well now you are ready to continue to the next step, which is solving Trigonometric Equations with a specified interval! How exciting right? I'll walk you through the the steps though, so don't be worried.

THINGS TO REMEMBER:
- Special triangles
-Quadrantal Angles
SOH CAH TOA
-CAST rule
- ΘR angles

Example 1
To solve for  Θ:
1) See if the interval is set in either radians or degrees. That will determine how you will write your final answer. 

2)Simplify the equation by isolating the unknown, which is the theta, and factor.

3)Find  ΘR 

and find the quadrants that the answer is in using the CAST rule.

4)Find values for  Θ in degrees or radians. 

Since the interval is in degrees, I will keep it my answer in degrees. 

You see how there are two answers? That's because there are two quadrants that my answer for  Θ could be in! 

* If there is a particular restriction, such as " Where sin  Θ> 0" in  a question such as " tan Θ= -1/√ 3 " tan would be possible in TWO quadrants, Q. 2 and 4. BUT because of restriction, sin cannot be in Q. 4, only Q. 2 therefore there will only be ONE answer.*

Here is the full question for you! 

So I hope that this gave you a little more understanding about solving trigonometric equations with a specific interval. Try to review your note as well, as they are very useful and important! 

Enjoy my fellow Pre calc mates!