Use trigonometric function values of quadrantal angles to evaluate each expression. (sin 180°)² + (cos 180°)²

Verified step by step guidance

1. Identify the trigonometric function values for the quadrantal angle 180°. Recall that \( \sin 180° = 0 \) and \( \cos 180° = -1 \).
2. Substitute these values into the expression \((\sin 180°)^2 + (\cos 180°)^2\).
3. Calculate \((\sin 180°)^2\) by squaring the sine value: \((0)^2 = 0\).
4. Calculate \((\cos 180°)^2\) by squaring the cosine value: \((-1)^2 = 1\).
5. Add the results from the previous steps: \(0 + 1\).

Key Concepts

Quadrantal Angles

Quadrantal angles are angles that are multiples of 90 degrees, specifically 0°, 90°, 180°, and 270°. At these angles, the sine and cosine functions take on specific values that are easy to remember: sin(0°) = 0, sin(90°) = 1, sin(180°) = 0, sin(270°) = -1, and cos(0°) = 1, cos(90°) = 0, cos(180°) = -1, cos(270°) = 0.

Trigonometric Function Values

The sine and cosine functions are fundamental in trigonometry, representing the ratios of the sides of a right triangle. For quadrantal angles, these functions yield specific values: for example, sin(180°) = 0 and cos(180°) = -1. Understanding these values is crucial for evaluating expressions involving trigonometric functions.

Pythagorean Identity

The Pythagorean identity states that for any angle θ, (sin θ)² + (cos θ)² = 1. This identity is essential in trigonometry as it relates the sine and cosine of an angle. In the context of the given expression, substituting the values of sin(180°) and cos(180°) into this identity helps confirm the evaluation of the expression.