Trigonometric Functions and Simplifications

The video tutorial explains how to simplify a trigonometric expression by multiplying and squaring sine and cosine terms, converting cotangent, and simplifying the denominator. It involves calculating products and differences to reach the final simplified expression, which is negative one half tangent t.

What is the first step in simplifying the given trigonometric expression?

• Convert cotangent to sines and cosines

• Multiply the numerator and denominator

• Perform a substitution for sine 2t

• Square the entire expression

How many factors of sine t minus cosine t are there in the numerator?

• One

• Two

• Three

• Four

What is cotangent t equal to in terms of sines and cosines?

• Cosine t divided by sine t

• Sine t divided by cosine t

• Sine t times cosine t

• Tangent t

What is the result of sine t times sine t?

• Tangent t

• Sine squared t

• Cosine squared t

• Sine t

What is the result of negative cosine t times negative cosine t?

• Negative sine squared t

• Positive cosine squared t

• Negative cosine squared t

• Zero

What happens when sine t is divided by sine t in the denominator?

• It becomes negative

• It remains unchanged

• It simplifies to one

• It simplifies to zero

What is the final simplified form of the expression?

• Negative one half cosine t

• Negative one half tangent t

• Negative one half sine t

• Negative one half cotangent t

What common factor is canceled between the numerator and denominator in the final step?

• Tangent t

• Cosine t

• Sine t

• Cotangent t

What is the result of negative four divided by eight?

• One half

• Negative one

• Zero

• Negative one half

What trigonometric function is represented by sine t divided by cosine t?

• Tangent t

• Cosecant t

• Secant t

• Cotangent t