Use trigonometric function values of quadrantal angles to evaluate each expression. (sec 180°)² ― 3 (sin 360°)² + cos 180°

Key Concepts

Quadrantal Angles

Quadrantal angles are angles that lie on the axes of the Cartesian coordinate system, specifically 0°, 90°, 180°, and 270°. The sine and cosine values of these angles are particularly straightforward, as they correspond to the coordinates of points on the unit circle. For example, at 180°, the coordinates are (-1, 0), leading to a cosine value of -1 and a sine value of 0.

Trigonometric Functions

Trigonometric functions, such as sine, cosine, and secant, relate the angles of a triangle to the ratios of its sides. The secant function is the reciprocal of the cosine function, meaning sec(θ) = 1/cos(θ). Understanding these functions is essential for evaluating expressions involving angles, especially when dealing with quadrantal angles where values are known.

Evaluating Expressions

Evaluating trigonometric expressions involves substituting known values of trigonometric functions into algebraic expressions. For the given expression, one must calculate the values of sec(180°), sin(360°), and cos(180°) using their respective known values, and then perform the arithmetic operations as indicated. This process is crucial for simplifying and solving trigonometric equations.