solve for B in the equation sin B= -2/4 where 180<B<270

Question

solve for B in the equation sin B= -2/4 where 180<B<270 

 

can you help me solve this problem algebra 2 with trig

Answer 1

First, find the reference angle, θ.  θ = Sin^-1(1/2) = 30°

 

Since we want an angle in the 3rd quadrant, the desired angle is 180° + θ = 210°

Answer 2

-2/4 can be reduced to -1/2.  SO you have

 

sinB = -1/2

 

B = -30

 

 

Since sine is negative in the 3rd and 4th quadrants, and B is in the 3rd quadrant,

 

B = 180 + 30