initial arm

terminal arm

θ

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.

vertex

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 =

Given that cos θ = and tan θ < 0, determine the quadrant in which θ lies.53

tan θ =

Trig Ratios for Angles Greater than 90°

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