Trigonometric Identities and Equations: Background You’ll Need 1

  • Evaluate sine and cosine functions at common points

sine and cosine

The sine and cosine functions describe coordinates on the unit circle, a circle of radius 1 centered at the origin.
For any angle [latex]\theta[/latex] measured in radians:
[latex]\sin(\theta) = y \quad \text{and} \quad \cos(\theta) = x[/latex]

Common angles on the unit circle: [latex]0, \frac{\pi}{6}, \frac{\pi}{4}, \frac{\pi}{3}, \frac{\pi}{2}[/latex]
The corresponding coordinates [latex](\cos\theta, \sin\theta)[/latex] are often memorized.

Find [latex]\sin\left(\frac{\pi}{3}\right)[/latex] and [latex]\cos\left(\frac{\pi}{3}\right)[/latex].

Find [latex]\sin(\pi)[/latex] and [latex]\cos(\pi)[/latex].

  1. Find [latex]\sin\left(\frac{\pi}{2}\right)[/latex] and [latex]\cos\left(\frac{\pi}{2}\right)[/latex].

  2. Find [latex]\sin\left(\frac{3\pi}{2}\right)[/latex] and [latex]\cos\left(\frac{3\pi}{2}\right)[/latex].

On the unit circle, sine corresponds to y-values and cosine to x-values.