Trigonometric Identities and Values

The video tutorial explains how to apply the sum and difference identities for trigonometric functions, specifically focusing on sine and cosine. It begins with an example using the sum identity for sine, demonstrating the substitution of angles and simplification of the expression. The tutorial then moves to a second example, which involves both the difference identity for sine and the sum identity for cosine. The instructor guides through the process of substituting angles, evaluating trigonometric functions using a reference triangle, and combining like terms to simplify the expression.

What is the sum identity for sine when applied to the expression sin(x + π/2)?

• cos(x)sin(π/2) + sin(x)cos(π/2)

• sin(x)sin(π/2) - cos(x)cos(π/2)

• cos(x)cos(π/2) - sin(x)sin(π/2)

• sin(x)cos(π/2) + cos(x)sin(π/2)

What is the value of cos(π/2)?

• -1

• 0

• 1

• Undefined

In the expression sin(x + π/2), what does it simplify to?

• sin(x)

• cos(x)

• -sin(x)

• -cos(x)

What is the first angle (A) in the second example involving sum and difference identities?

• π/3

• π/6

• π/4

• π/2

Which operation is used for the cosine identity in the second example?

• Division

• Addition

• Subtraction

• Multiplication

What is the sine of π/6?

• 0

• 1

• 1/2

• √3/2

What is the cosine of π/3?

• √3/2

• 0

• 1

• 1/2

How do you simplify 1/2 cos(y) + 1/2 cos(y)?

• 1/2 cos(y)

• cos(y)

• 0

• 2 cos(y)

What is the result of combining -√3/2 sin(y) - √3/2 sin(y)?

• -√3 sin(y)

• 0

• √3 sin(y)

• -2√3 sin(y)

What is the cosine of π/6?

• √3/2

• 1/2

• 0

• 1