trigonometry

Question

determine all angles theta with 0<theta<360 such that sin of theta ewuals -.7

Answer 1

First, remember that you can think of sine as a point's y-coordinate. This means that sine is positive in Quadrants I and II and sine is negative in Quadrants III and IV. Since you're looking for an angle with negative sine, you'll want to find two points, one in Quadrant III and one in Quadrant IV.

 

The first step is to find out what angle in Quadrant I has a sine of 0.7. If sin(θ) = 0.7, then θ = sin^-1(0.7) = 44.4º (rounded to the nearest tenth).

 

Next, you'll have to find angles that have equivalent sine values in Quadrants III and IV. You can do that by reflecting 44.4º over the x-axis and then the y-axis (for Quadrant III) and over just the x-axis (for Quadrant IV). This gives you two angles with sines of -0.7: (180 + 44.4)º = 224.4º in Quadrant III and (360 - 44.4)º = 315.6º in Quadrant IV.

Answer 2

sinθ = -7

 

θ = sin^-1(-0.7)

θ = -44.43

 

 

Sine is negative in the 3rd and 4th quadrant.

 

θ = 180 + 44.43            and           θ = 360 - 44.43 

 

θ = 224.43                    and            θ = 315.57