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Solving Trig Equations

You'll be needing to solve some trig equations at the very end of some Calculus problems...  So, let's review!
 


Solve		sin( theta ) = -square root( 3 ) / 2
Remember that this is asking for the theta where the
                    sine is-square root( 3 ) / 2That's long and negative!

ALWAYS draw a quick unit circle!

up and down guys , long , negative ... 4 * pi / 3 ... 5 * pi / 3Usually, you'll just need to find the solutions on ...  which is one lap around the unit circle.
 
So, forsin( theta ) = -square root( 3 ) / 2
theta = ( 4 * pi ) / 3ortheta = ( 5 * pi ) / 3

If you want ALL the solutions, remember that you add 2k * pi to get all the laps around

theta = ( 4 * pi / 3 ) + 2k * piortheta = ( 5 * pi / 3 ) + 2k * pi

YOUR TURN:

Solvecos( theta ) = -( 1 / 2 )on[ 0 , 2 * pi )

 

Solvecsc( theta ) = -square root( 2 )on[ 0 , 2 * pi )
*hint:

 

csc( theta ) = 1 / sin( theta )
find this!