The image contains a presentation slide on "Trigonometric Functions," specifically focusing on evaluating trigonometric functions exactly for special angle measures: $30^\circ$, $45^\circ$, and $60^\circ$.

Example:

The slide provides an example of evaluating trigonometric functions for a $30^\circ$ angle. It illustrates a right triangle with the following labels:

• Hypotenuse: The side opposite the right angle.
• Opposite: The side opposite the $30^\circ$ angle.
• Adjacent: The side adjacent to the $30^\circ$ angle.

Task:

The task is to evaluate the six trigonometric functions (sine, cosine, tangent, cosecant, secant, and cotangent) for the angle $30^\circ$.

Solution:

Given the right triangle with angle $30^\circ$:

• Sin(30°) = Opposite/Hypotenuse = 1/2
• Cos(30°) = Adjacent/Hypotenuse = $\sqrt{3}/2$
• Tan(30°) = Opposite/Adjacent = 1/$\sqrt{3}$

The reciprocals are:

• Csc(30°) = 1/Sin(30°) = 2
• Sec(30°) = 1/Cos(30°) = 2/$\sqrt{3}$
• Cot(30°) = 1/Tan(30°) = $\sqrt{3}$

Would you like any additional details or explanations?

5 Related Questions:

1. How do you derive the exact values of trigonometric functions for a $45^\circ$ angle?
2. What is the significance of special triangles in trigonometry?
3. Can you explain why the sine of $30^\circ$ is $1/2$?
4. How do the trigonometric ratios change for an angle of $60^\circ$?
5. How can you use the unit circle to evaluate trigonometric functions for these special angles?

Tip:

Remember that understanding the properties of the 30°-60°-90° triangle is key to quickly solving problems involving these specific angles in trigonometry.