Trigonometric Functions and Identities

This video tutorial explains how to evaluate trigonometric expressions using sum and difference identities for sine and cosine. It covers the evaluation of sine(x - 90 degrees) and cosine(180 degrees + x) using these identities, with a review of relevant trigonometric values from the unit circle. The tutorial provides step-by-step calculations and simplifications, resulting in expressions for negative cosine x in both cases.

What is the purpose of using sum and difference identities in trigonometry?

• To simplify complex numbers

• To evaluate trigonometric expressions

• To solve quadratic equations

• To find the area of a triangle

In the expression sine of (x - 90 degrees), what is the value of 'b'?

• 0 degrees

• 180 degrees

• 90 degrees

• x

What is the value of cosine 90 degrees?

• 1

• 0

• Undefined

• -1

What is the value of sine 90 degrees?

• -1

• 0

• Undefined

• 1

What does sine of (x - 90 degrees) simplify to?

• -sine x

• sine x

• -cosine x

• cosine x

In the expression cosine of (180 degrees + x), what is the value of 'a'?

• x

• 90 degrees

• 180 degrees

• 0 degrees

What is the value of cosine 180 degrees?

• 0

• Undefined

• 1

• -1

What is the value of sine 180 degrees?

• 0

• 1

• -1

• Undefined

What does cosine of (180 degrees + x) simplify to?

• -sine x

• sine x

• -cosine x

• cosine x

What is the significance of the unit circle in evaluating trigonometric functions?

• It helps in solving linear equations

• It is used to calculate the area of a circle

• It is irrelevant to trigonometry

• It provides values for trigonometric functions at specific angles