Find a cofunction with the same value as the given expression.
cos (𝜋/2)

Verified step by step guidance

1. Understand the concept of cofunctions: In trigonometry, cofunctions are pairs of trigonometric functions that are equal when their angles are complementary. Complementary angles add up to $\frac{\pi }{2}$ radians or 90 degrees.
2. Identify the cofunction pair: The cosine function $\cos (\theta )$ and the sine function $\sin (\theta )$ are cofunctions. This means that $\cos (\theta )=\sin (\frac{\pi }{2}-\theta )$.
3. Apply the cofunction identity: For the given expression $\cos (\frac{\pi }{2})$, use the cofunction identity to find the equivalent sine expression. Substitute $\theta =\frac{\pi }{2}$ into the identity: $\cos (\frac{\pi }{2})=\sin (\frac{\pi }{2}-\frac{\pi }{2})$.
4. Simplify the expression: Calculate $\frac{\pi }{2}-\frac{\pi }{2}$ to simplify the angle inside the sine function.
5. Conclude with the cofunction: The expression $\sin (0)$ is the cofunction with the same value as $\cos (\frac{\pi }{2})$.

Key Concepts

Cofunctions in Trigonometry

Cofunctions are pairs of trigonometric functions that are related through complementary angles. For example, the sine function is the cofunction of cosine, meaning sin(θ) = cos(90° - θ). This relationship is crucial for finding equivalent values of trigonometric expressions when angles are complementary.

Value of Cosine at Specific Angles

The cosine function has specific values at key angles, such as 0°, 30°, 45°, 60°, and 90°. For instance, cos(90°) equals 0. Understanding these values helps in evaluating trigonometric expressions quickly and accurately, especially when dealing with angles in radians, such as π/2.

Radians and Degrees

Trigonometric functions can be expressed in both degrees and radians. Radians are a unit of angular measure where π radians equals 180 degrees. Recognizing the conversion between these two systems is essential for solving trigonometric problems, as it allows for the correct interpretation of angles in various contexts.