1. Lesson 3

1.3. Explore 2

Mathematics 20-1 Module 2

Module 2: Trigonometry

 

Using Special Triangles to Find Angles

 

This is a play button that opens Finding Trigonometric Ratios for 30° and 60° Angles Without Technology.

In Try This 2 you saw how cosine, sine, and tangent can be determined for a 45° angle without using technology. Watch Finding Trigonometric Ratios for 30° and 60° Angles Without Technology.

You can now create a very basic table of trigonometric values based on the ratios found using

  • angles with terminal arms that lie on the x- or y-axis of a circle (0°, 90°, 180°, 270°, and 360°)

  • angles found in special triangles (30°, 45°, 60°)
θ cos θ sin θ tan θ
0° 1 0 0
30°
45° 1
60°
90° 0 1 undefined
180° −1 0 0
270° 0 −1 undefined
360° 1 0 0

 

This is a play button that opens Using a 30-60-90 Triangle for a 150° Angle.

So far you have used these special triangles only for angles in the first quadrant (0° ≤ θ ≤ 90°). These triangles can be used to find angles in other quadrants too. The key is to use one of these special triangles to determine the coordinates of a point on the terminal arm of the angle in question. Watch Using a 30-60-90 Triangle for a 150° Angle.

This is a play button that opens Using a 30-60-90 Triangle for a 300° Angle.

Sometimes it’s not as obvious to see how to use one of the special triangles. Watch Using a 30-60-90 Triangle for a 300° Angle to see how a similar process can be used for a 300° angle.