Trigonometric Functions and Identities

The video tutorial covers quotient identities in trigonometry, focusing on tangent and cotangent. It explains how tangent is the ratio of sine to cosine, and cotangent is the reciprocal. The tutorial provides examples of calculating these values using given sine and cosine values. It also explores the unit circle to find tangent values at specific angles and discusses the behavior of tangent and cotangent at special angles, including when they are undefined.

What is the quotient identity for tangent in terms of sine and cosine?

• Tangent is cosine minus sine

• Tangent is cosine over sine

• Tangent is sine over cosine

• Tangent is sine times cosine

If sin(θ) = 4/5 and cos(θ) = 3/5, what is tan(θ)?

• 5/3

• 4/3

• 3/5

• 3/4

How can you simplify a complex fraction like (4/5) / (3/5)?

• Multiply both numerator and denominator by 5

• Add 5 to both numerator and denominator

• Subtract 5 from both numerator and denominator

• Divide both numerator and denominator by 5

What is the value of tan(π/4) using the unit circle?

• √2

• 1

• Undefined

• 0

In which quadrant is 2π/3 located, and what is the sign of tan(2π/3)?

• Quadrant 1, positive

• Quadrant 3, negative

• Quadrant 2, positive

• Quadrant 2, negative

What is the value of cot(4π/3) in terms of √3?

• -√3

• -1/√3

• 1/√3

• √3

How do you find the reference angle for an angle in quadrant 3?

• Subtract the angle from 180 degrees

• Subtract the angle from 360 degrees

• Subtract 360 degrees from the angle

• Subtract 180 degrees from the angle

What is the value of tan(0 degrees)?

• Infinity

• 0

• 1

• Undefined

Why is tan(90 degrees) undefined?

• Because the sine value is zero

• Because the cosine value is zero

• Because both sine and cosine are zero

• Because the angle is not on the unit circle

What is the value of cot(180 degrees)?

• Undefined

• 1

• -1

• 0