Video narration
Six formulas can feel like six separate rules. But they're really built from one familiar move: flipping a fraction. If two thirds becomes three halves, you've taken its reciprocal—swapped numerator and denominator. In trigonometry, the same idea connects each right-triangle ratio to its partner. That's the turn: these six formulas are not separate facts. Each comes from flipping its matching ratio. Sine and cosecant form one pair: sine theta equals one over cosecant theta, and vice versa. Cosine and secant work the same way: cosine theta equals one over secant theta, and vice versa. Tangent and cotangent complete the pattern: tangent theta equals one over cotangent theta, and vice versa. So if an identity slips away, flip the ratio to rebuild it. These reciprocal identities apply wherever the expressions are defined. Remember the three pairs as one pattern: sine-cosecant, cosine-secant, tangent-cotangent.