Trigonometric Expressions Simplification

This video tutorial covers the simplification of trigonometric expressions. It begins with an introduction to the concept of simplifying trig expressions by rewriting them in terms of one trig function. The video demonstrates techniques such as using sines and cosines and applying Pythagorean identities. Two examples are provided to illustrate these methods, showing step-by-step simplification processes. The tutorial emphasizes the importance of rewriting expressions and using identities to achieve simplification.

What is the primary goal when simplifying a trigonometric expression?

• To write it in terms of one trigonometric function

• To eliminate all trigonometric functions

• To convert it into a polynomial

• To express it in terms of exponential functions

Which technique is suggested if there is no obvious substitution in simplifying trigonometric expressions?

• Use exponential functions

• Convert to polar coordinates

• Use logarithmic identities

• Write everything in terms of sines and cosines

Which trigonometric function is cotangent x rewritten as?

• 1 / Cosine x

• 1 / Sine x

• Sine x / Cosine x

• Cosine x / Sine x

What is the result of simplifying the expression with cotangent and cosecant in the first example?

• Sine x

• Tangent x

• Cosine x

• Secant x

What happens to the sine squared x terms in the first example?

• They remain unchanged

• They are multiplied

• They cancel each other out

• They are added together

In the second example, which identity is primarily used to simplify the expression?

• Half Angle Identities

• Pythagorean Identities

• Double Angle Identities

• Sum and Difference Identities

What is tangent squared t rewritten as in terms of sines and cosines?

• 1 / Sine squared t

• 1 / Cosine squared t

• Cosine squared t / Sine squared t

• Sine squared t / Cosine squared t

What is the first step in simplifying the second example?

• Convert to exponential form

• Use the double angle formula

• Rewrite tangent squared t in terms of sines and cosines

• Apply the sum and difference identities

What is the simplified result of the expression in the second example?

• 1

• 2

• -1

• 0

What is the final form of the expression in the second example?

• Negative one

• Negative sine squared t

• Zero

• Cosine squared t