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Coolmath Precalculus Review Calculus Preview
Lesson 31 - Trigonometry - Solving Trig Equations (page 3 of 3)
---- This Precalculus review (Calculus preview) lesson reviews how to solve the type of trig equations that come up in Calculus.

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One more:

Solve tan( 3x ) = 1
 
Remember the game on these...  We know how to solve
tan( theta ) = 1 ...  So, let's do that.

 

tan( theta ) = 1 This 1 means that sine and cosine are the same!

 
start at pi / 4  ...  go around pi  ...  5 * pi / 4

sin( theta ) / cos( theta ) = 1

So,
 
theta = ( pi / 4 ) + k * pi
Just go pi around and you pick up the other one.

But, we needed to solve for x, not theta.  Stick the 3x back in for the theta:

theta = ( pi / 4 ) + k * pi  ...  3x = ( pi / 4 ) + k * pi  ...  divide by 3  ...  x = ( pi / 12 ) + ( k * pi / 3 )

You can always check this solution on a graphing calculator by graphing

tan( 3x ) = 1  ...  y = tan( 3x )  and  y = 1
 

at the same time.  They should intersect at x = ( pi / 12 ) and every
pi / 3 interval from there.        

 


TRY IT:

Solve cos( 3x ) = square root( 3 ) / 2

 


 The printing and distribution and/or downloading of these lessons is strictly prohibited.

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