Instructions
Read each question carefully and provide your answers in the space provided. Show your work where necessary.
1. Basic Trigonometric Ratios
Using a right triangle, if the length of the opposite side is 3 units and the length of the hypotenuse is 5 units, calculate:
a) The sine of the angle θ (sin θ).
b) The cosine of the angle θ (cos θ).
c) The tangent of the angle θ (tan θ).
2. Solving for an Angle
Find the measure of angle θ if:
a) sin θ = 0.5
b) cos θ = 0.6
c) tan θ = 1.
3. Word Problem
A ladder is leaning against a wall. The foot of the ladder is 4 feet from the wall, and the ladder reaches a height of 3 feet on the wall. Find the angle θ between the ground and the ladder.
4. Trigonometric Identities
Complete the following identities by filling in the blanks:
a) sin² θ + cos² θ =
b) tan θ = sin θ / cos θ
c) 1 + tan² θ =
5. Graphing Trigonometric Functions
Sketch the graph of the sine function for one complete cycle (0 to 2π). Describe its amplitude and period.