Understanding Tangent Identities

This video tutorial covers the sum and difference identities for tangent, demonstrating how to use these identities to calculate function values. It includes examples of finding the tangent of -105 degrees and angles in radians, and concludes with simplifying tangent PI - theta using an identity.

What is the formula for the tangent of the sum of two angles?

• Tangent A + Tangent B divided by 1 + Tangent A x Tangent B

• Tangent A x Tangent B divided by 1 + Tangent A + Tangent B

• Tangent A - Tangent B divided by 1 + Tangent A x Tangent B

• Tangent A + Tangent B divided by 1 - Tangent A x Tangent B

How can the tangent sum and difference identities be combined?

• By subtracting the identities from each other

• By adding the identities together

• By using separate formulas for each identity

• By using a single formula with a +/- in the numerator and denominator

What is the first step in proving the tangent sum identity?

• Using the cosine identity

• Remembering that tangent theta is sine theta divided by cosine theta

• Using the difference identity

• Applying the Pythagorean theorem

How do you express -105 degrees using reference angles?

• -120 degrees + 15 degrees

• -90 degrees + 15 degrees

• -60 degrees - 45 degrees

• -75 degrees - 30 degrees

What is the simplified form of the tangent of -105 degrees after rationalization?

• Square root 3 + 2

• Negative square root 3 - 2

• Square root 3 - 2

• Negative square root 3 + 2

What is the reference angle in degrees for 5π/12?

• 45 degrees

• 90 degrees

• 60 degrees

• 75 degrees

What is the tangent of π/4?

• 1

• 1/2

• 0

• Square root 3

What is the result of rationalizing the denominator for tangent 5π/12?

• 2 + square root 3

• 1 + square root 3

• 2 - square root 3

• 1 - square root 3

How is tangent(π - θ) expressed as a single function of θ?

• Negative tangent θ

• Tangent θ

• Zero

• Tangent π

What is the value of tangent π on the unit circle?

• Undefined

• 1

• -1

• 0