Trigonometric Identities & Equations

What you'll learn

Trig ratios of any angle using the CAST rule and reference angles, the Pythagorean identity, and solving trig equations over a range (including quadratics in sinθ/cosθ).

• The CAST rule tells you which ratio is positive in each quadrant
• The reference angle is the acute angle to the x-axis
• The Pythagorean identity links sine and cosine of the SAME angle
• \(\tan\theta = \dfrac{\sin\theta}{\cos\theta}\) connects the third ratio to the first two
• Solving \(\sin\theta=k\) or \(\cos\theta=k\) over a range means finding EVERY solution, not just one
• A quadratic in \(\sin\theta\) or \(\cos\theta\) is solved by substitution first, THEN trig