Evaluate the following trig problems:

Question

a) If sinX = .655  , find X such that 90<X<180

 

b) Find all possible values of X between 0^o and 360^o if cosX = -.3456

 

c) Why is there more than just one answer for part b?

 

d) Find all possible values of X , if sinX = .1746

Answer 1

a) sin^-1 0.655 = 40.9°, in QII 139.1°

 

b) cos^-1 -0.3456 = 110.2° and 249.8°

 

c) Cosine is negative in QII andQIII

 

d) sin^-1 0.1746 = 10° and 170°

Answer 2

a)

    sin(x)=.655

         x=40.9 degrees

     but since      90<x<180

  so x= 180-40.9=139.1 degrees

   x=139.1 degrees

b)

  cos(x)=-.3456

Since cos(x) is negative it will be either in second or third quadrant.

   x=110.2. degrees. Or. 249.8 degrees

c)

Because cos(x) is negative in second and third quadrant

 

d)

 

sin(x)=.1746

Sin(x) is positive in first and second quadrant

x=10.05 degrees  OR  x= 169.95  degrees