Reciprocal Trig Identities

Sine and cosine come from the coordinates of a point on the unit circle, while secant and cosecant are defined as their reciprocals. That means secant gives the "1 divided by cosine" value, and cosecant gives "1 divided by sine," so they are only defined when the denominator is not zero. These identities are useful because they let you rewrite expressions in terms of sine and cosine, which are often easier to simplify and analyze.

Use these identities when simplifying trigonometric expressions, solving trig equations, or converting between different trig functions. They also appear often in calculus and physics when you need to express a result using reciprocal trig functions.

• Swapping secant with cosine or cosecant with sine instead of using the reciprocal
• Forgetting to check whether sin θ or cos θ equals zero before dividing
• Rounding too early and losing the exact value when a surd form is expected