Solving Trig Equations

“Solving trig equation is no different than solving ‘normal’ equation, just with an extra flavor of trigonometry”

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Normally, if you see an equation like:

7390128340937 = 10923x + 3092418

It DOESN’T matters how complicated they look, you will still try to solve for the x. One of the ways you probably use to solve for x is isolating the x term, then solve for x.

So, let’s say you to solve this oh-so-complicated equation:  

0 = 2sin(theta) - 1 Give theta within [0, 360]

      First thing we must do is isolate the theta term. 

(     add 1 and divide the whole equation by 2)

o  (1/2) = sin theta 

When you have finished isolating the term, try solving for the (theta)

o   ( 1/2) = sin(theta)

o   arcsin ( 1/2) = theta

o   30 degrees, 150 degrees = theta

	Since:sin ( 30 degrees ) = ( 1/2 ) and sin ( 150 degrees ) = ( 1/2 )  Arcsin of ½ will be 300 and 1500.  However, if you didn’t know this, you can still just plug it  into your calculator. Of course, you would only list theta within [0, 360]  since there is many degrees outside the interval [0, 360]  that would work for the equation, like 390 degrees or 510 degrees.

 

-TrigInADay