Trigonometric Identities and Functions

This video tutorial covers section 5.1, focusing on trigonometric identities. It begins with an introduction to identities, explaining their significance and the need to memorize certain ones. The tutorial then delves into negative angle identities, reciprocal and quotient identities, and Pythagorean identities, providing examples and explanations for each. The final section focuses on simplifying trigonometric expressions using these identities, emphasizing the importance of writing expressions in terms of sine and cosine.

What is an identity in mathematics?

• An equation that is true only for integers

• An equation that is never true

• An equation true for all values of the variable

• An equation true for some values of the variable

Which of the following is a negative angle identity for sine?

• sin(-θ) = sin(θ)

• sin(-θ) = -sin(θ)

• sin(-θ) = -cos(θ)

• sin(-θ) = cos(θ)

If tan(θ) = 2.6, what is tan(-θ)?

• 1

• 0

• -2.6

• 2.6

What is the reciprocal of the tangent function?

• Cotangent

• Cosecant

• Cosine

• Secant

Which identity represents tan(θ) in terms of sine and cosine?

• tan(θ) = sin(θ) / cos(θ)

• tan(θ) = cos(θ) / sin(θ)

• tan(θ) = 1 / sin(θ)

• tan(θ) = 1 / cos(θ)

What is the Pythagorean identity involving sine and cosine?

• sin²(θ) + cos²(θ) = 1

• sin²(θ) - cos²(θ) = 0

• sin²(θ) - cos²(θ) = 1

• sin²(θ) + cos²(θ) = 0

In which quadrant is cosine positive and tangent negative?

• Quadrant III

• Quadrant II

• Quadrant IV

• Quadrant I

How can you simplify the expression sec²(θ) - 1?

• cot²(θ)

• tan²(θ)

• csc²(θ)

• 1