solve problem

Question

GIVEN THE FUNCTION VALUE AND THE QUADRANT RESTRICTION. FIND θ?

 

CSC θ = -1.0403,   INTERVAL (270°, 360°)

 

 

Answer 1

CSC θ = -1.0403

 

Co-secant is the inverse of the sine function.

 

SIN θ = -1/1.0403

 

θ = -74 degrees

 

Add 360 degrees to this answer

 

θ = 286 degrees

Answer 2

The interval tells us this is the 4th quadrant. So sin θ = 1/-1.0403 = -0.96126.

 

So θ = sin^-1 -0.96126 = - 74^O (clockwise), so that's 360 - 74 = 286^O