Download Trig Ratios for Angles Greater than 90°

Trig Ratios for Angles Greater than 90°
terminal arm
vertex
θ
initial arm
Standard position: initial arm lies on the positive x-axis and the vertex is at the origin.
Principal angle: counterclockwise angle measured from the initial arm to the terminal
arm; its value is between 0° and 360°.
Related acute angle: acute angle between the terminal arm and the x-axis.
Determine the related acute angle in each diagram.
75°
160°
250°
345°
→ If the terminal arm lies in Quadrant II, the related acute angle is ___________.
→ If the terminal arm lies in Quadrant III, the related acute angle is ____________.
→ If the terminal arm lies in Quadrant IV, the related acute angle is ____________.
If the angle between the terminal arm and initial arm is 255°, find the related acute
angle.
The point P(-3, 4) lies on the terminal arm of a principal angle. Determine the primary
trigonometric ratios, and the principal angle to the nearest degree.
Determine the quadrant(s) in which each trigonometric ratio is positive.
sin θ =
cos θ =
tan θ =
Given that cos θ = 3 and tan θ < 0, determine the quadrant in which θ lies.
5
Use the point P(0, 1) to determine the values of the primary trig ratios for 90°.
Determine the possible values of θ if csc θ = 
2
.
3