Q1. Find the 6 trigonometric ratios of for the triangle below:

Background

Topic: Right Triangle Trigonometry

This question tests your understanding of how to find the six basic trigonometric ratios (sine, cosine, tangent, cosecant, secant, and cotangent) for a given angle in a right triangle.

Key Terms and Formulas

• Opposite side: The side opposite the angle .

• Adjacent side: The side next to the angle (but not the hypotenuse).

• Hypotenuse: The longest side of the right triangle (opposite the right angle).

The six trigonometric ratios are:

Step-by-Step Guidance

1. Identify the sides of the triangle relative to . In the diagram, the side labeled 2 is adjacent to $\theta$, the hypotenuse is 3, and the opposite side is currently unknown.

2. Use the Pythagorean Theorem to find the length of the missing side (opposite to ):

   Let be the unknown side, , and .

3. Substitute the known values and solve for the missing side:

4. Once you have the length of the opposite side, write the six trigonometric ratios using the definitions above.

Try solving on your own before revealing the answer!