Trigonometric equations on a specified interval 1

In class on monday we have learned about trigonometric equations on a specified interval 1. We have done this in grade 11 but in this class we have learned how to do without using calculator.

To find out solve the equation first. Select possible quadrant using CAST rule. Than check the interval given. By using the soh cah toa determine the reference angle by substituting the value of Sin θ = Opposite/Hypotenuse in a triangle in selected quadrant for this example. In last by using 3 simple steps we can find the related angle.

Finding related angles:
Quadrant 1= reference angle = related angle
Quadrant 2= related angle = 180°-ref. angle
Quadrant 3= rel. Angle= 180+ ref. angle
Quadrant 4= rel.angle=360-ref. angle
For example :
2 sin θ= 1 over the interval 0° ≤ θ ≤ 360°
2 sin θ= 1
sin θ= ½
Sin θ = Opposite/Hypotenuse
opposite=1
Hypotenuse=2
sin θ = 30°

Quadrant 1= 30° Quadrant 2= 180°-30°=150°