Trigonometric Identities and Functions

This video tutorial covers the properties of trigonometric functions, focusing on reciprocal, quotient, and Pythagorean identities. It explains how to derive these identities and apply them to solve trigonometric problems. The video also discusses the significance of these identities in determining trigonometric function values and provides examples to illustrate their application.

Which of the following is a reciprocal identity for sine?

• sin(θ) = 1/sec(θ)

• sin(θ) = 1/cos(θ)

• sin(θ) = 1/cot(θ)

• sin(θ) = 1/tan(θ)

Tags

CCSS.HSF.TF.C.8

If cos(θ) = 2/3, what is sec(θ)?

• 3/2

• 2/3

• 1/5

• 5/2

Tags

CCSS.HSF.TF.C.8

What is the cotangent of θ if tan(θ) = 5?

• 1/5

• 5

• 1/2

• 2

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

• tan(θ) = cos(θ) / sin(θ)

• tan(θ) = sin(θ) / cos(θ)

• tan(θ) = 1 / sin(θ)

• tan(θ) = sin(θ) * cos(θ)

Tags

CCSS.HSF.TF.C.8

What is the Pythagorean identity involving sine and cosine?

• cos^2(θ) - sin^2(θ) = 1

• sin^2(θ) - cos^2(θ) = 1

• sin^2(θ) + cos^2(θ) = 1

• sin^2(θ) + tan^2(θ) = 1

Tags

CCSS.HSF.TF.C.8

If sin(θ) = 3/5 and θ is in the second quadrant, what is the sign of tan(θ)?

• Positive

• Negative

• Zero

• Undefined

Tags

CCSS.HSF.TF.C.8

Given tan(θ) = 5/12 in the third quadrant, what is the sign of sin(θ)?

• Positive

• Negative

• Zero

• Undefined

Tags

CCSS.HSF.TF.C.8

How do you find sin(θ) using the Pythagorean identity if cos(θ) = 3/5?

• sin(θ) = 1 + cos^2(θ)

• sin(θ) = cos^2(θ) - 1

• sin(θ) = 1 - cos^2(θ)

• sin(θ) = √(1 - cos^2(θ))

Tags

CCSS.HSF.TF.C.8

What is the value of r if x = -12 and y = -5 in the third quadrant?

• 12

• 17

• 5

• 13

Tags

CCSS.HSF.TF.C.8

If tan(θ) = 5/12, what is the value of sin(θ) in the third quadrant?

• -5/13

• 5/13

• -12/13

• 12/13

Tags

CCSS.HSF.TF.C.8