Trigonometric Equations

what's up everyone

          

           In class, we discussed about unit circles, and special triangles. Right now I wanted to show how can you find the theta in trigonometric equation if there's an interval that is given.

NOTE: SINθ,COSθ,TANθ can be X 

Steps to solve for theta  "θ"

• Simplify by isolating the trigonometric ratio or factoring
• Determine the reference angle 
• Cast rule is very important!!!!!!!!!!!!!!!!!!!!!!!!!!!!
• Check the interval given
• State values for "θ" in degrees or radian

Example: solve for "θ" over the indicated interval.

a) 2sin²θ=3sinθ-1, interval 0 <(or equal) θ <(or equal) 2(pi)---------->

-Plug in x for sine to understand the equation------->

-The sine theta equals 1/2 is positive on quadrant 1 and 2

-Sine theta equals 1 is quadrantal angle which is π/2

-The theta R is π/6

-π/6 is from quadrant 1 and 5π/6 is from quadrant 2