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

Verified step by step guidance

1. Recall the cofunction identity that relates cosine and sine: \(\cos\left(\frac{\pi}{2} - x\right) = \sin x\).
2. Identify the angle in the given expression: here, the angle is \(\frac{\pi}{2}\).
3. Set up the equation to find the cofunction: we want to express \(\cos\left(\frac{\pi}{2}\right)\) as \(\sin\) of some angle \(x\) such that \(\cos\left(\frac{\pi}{2}\right) = \sin x\).
4. Using the identity, rewrite \(\cos\left(\frac{\pi}{2}\right)\) as \(\sin\left(\frac{\pi}{2} - \frac{\pi}{2}\right)\), which simplifies to \(\sin 0\).
5. Thus, the cofunction with the same value as \(\cos\left(\frac{\pi}{2}\right)\) is \(\sin 0\).

Key Concepts

Cofunction Identity

Cofunction identities relate the trigonometric functions of complementary angles, where the sum of the angles is π/2 radians (90°). For example, cosine of an angle equals the sine of its complement: cos(θ) = sin(π/2 - θ). This concept helps find equivalent expressions using different trig functions.

Value of Cosine at π/2

The cosine function at π/2 radians (90°) equals zero. This is a fundamental value on the unit circle, where the point corresponding to π/2 is (0,1), so cos(π/2) = 0. Knowing this helps verify or simplify trigonometric expressions.

Unit Circle and Angle Measurement

The unit circle is a circle with radius 1 centered at the origin, used to define trigonometric functions for all angles. Angles are measured in radians, where π radians equals 180°. Understanding the unit circle allows visualization of sine and cosine values and their relationships.