Focus on finding values of specific angles, specifically for:
30-60-90 Triangle
45-45-90 Triangle
Tasks include:
Finding the exact values of trigonometric functions for 30°, 45°, and 60°.
Utilizing a calculator for approximating trigonometric function values.
Solving applications using trigonometric functions.
Exact Values of Trigonometric Functions
Determine the exact six trig values for the following angle measures:
60° (𝜋/3)
30° (𝜋/6)
45° (𝜋/4)
Specific Functions:
sin 60°, cos 60°, tan 60°, cot 60°, csc 30°, sec 30°, etc.
Examples
Use pre-calculated values to simplify the following expressions:
a. sin 45° cos 30°
b. tan 𝜋/4 − sin 𝜋/3
c. tan² 𝜋/6 + sin² 𝜋/4
d. 4 cos 45° − 2 sin 45°
e. 1 − cos² 30° − cos² 60°
f. csc² 𝜋/3 − 5
g. sin 𝜋/4 + cos 𝜋/4 − 2
h. sec 60° − cos 60° + tan 60°
Using a Calculator
Ensure that the calculator is set to the correct mode (Radians or Degrees):
a. cos 48°
b. csc 21°
c. tan 𝜋/12
d. sin 35°
e. cot 103°
f. sec (4/5)𝜋
Applications of Trigonometry
Angle of Elevation & Depression:
Example 1:
The angle of elevation of the Sun is 35.1°. The shadow of the Washington Monument measures 789 feet long. Calculate the height of the monument.
Example 2:
A pilot in a helicopter observes a landing pad below. If the angle of depression is 73° and the horizontal distance to the pad is 1,200 feet, determine the helicopter's altitude.
Draw a diagram and label the components to assist in calculation.