Trigonometric Identities and Simplifications

The video tutorial explains how to simplify trigonometric expressions by converting them into sines and cosines using reciprocal identities. It provides four examples: simplifying tangent x times cosine x to sine x, cosecant x times cosine x to cotangent x, sine x times cotangent x to cosine x, and secant x times cosine x to one. Each example demonstrates the process of identifying common factors and simplifying the expressions step-by-step.

What is the first step in simplifying trigonometric expressions?

• Use the Pythagorean identities

• Convert to sines and cosines

• Use the angle sum identities

• Convert to tangent and cotangent

What does the expression tangent x times cosine x simplify to?

• Cosine x

• Sine x

• Tangent x

• Cotangent x

Which identity is used to simplify tangent x in the expression tangent x times cosine x?

• Tangent x = 1 / cosine x

• Tangent x = sine x / cosine x

• Tangent x = cosine x / sine x

• Tangent x = 1 / sine x

What does the expression cosecant x times cosine x simplify to?

• Secant x

• Cotangent x

• Tangent x

• Sine x

Which identity is used to express cosecant x in the expression cosecant x times cosine x?

• Cosecant x = 1 / cosine x

• Cosecant x = sine x / cosine x

• Cosecant x = cosine x / sine x

• Cosecant x = 1 / sine x

What does the expression sine x times cotangent x simplify to?

• Secant x

• Tangent x

• Cosine x

• Sine x

Which identity is used to express cotangent x in the expression sine x times cotangent x?

• Cotangent x = sine x / cosine x

• Cotangent x = 1 / sine x

• Cotangent x = cosine x / sine x

• Cotangent x = 1 / cosine x

What does the expression secant x times cosine x simplify to?

• Tangent x

• One

• Sine x

• Zero

Why does the expression secant x times cosine x simplify to one?

• They are complementary functions

• They are reciprocal functions

• They are inverse functions

• They are equal functions

Which identity is used to express secant x in the expression secant x times cosine x?

• Secant x = 1 / sine x

• Secant x = cosine x / sine x

• Secant x = 1 / cosine x

• Secant x = sine x / cosine x