Trigonometric Functions and Identities

The video tutorial covers the double angle formulas for sine, cosine, and tangent. It explains how to derive these formulas and apply them to solve problems. The tutorial includes example problems where the values of sine, cosine, and tangent are calculated using given angles. It also demonstrates how to use double angle formulas to solve expressions involving angles like 75 and 15 degrees. The video emphasizes understanding the formulas and applying them to various trigonometric problems.

What is the double angle formula for sine?

• sin(2θ) = 2tan(θ)/(1 - tan²(θ))

• sin(2θ) = 1 - 2sin²(θ)

• sin(2θ) = sin²(θ) - cos²(θ)

• sin(2θ) = 2sin(θ)cos(θ)

How is the double angle formula for cosine expressed?

• cos(2θ) = 1 - 2sin²(θ)

• cos(2θ) = 2cos²(θ) - 1

• cos(2θ) = cos²(θ) + sin²(θ)

• cos(2θ) = cos²(θ) - sin²(θ)

If sin(θ) = 3/5 and θ is in the first quadrant, what is sin(2θ)?

• 7/25

• 4/5

• 24/25

• 3/5

Given cos(θ) = 5/13 in the fourth quadrant, what is cos(2θ)?

• 120/169

• 144/169

• -119/169

• 25/169

What is the value of tan(2θ) if tan(θ) = -12/5?

• 120/119

• -24/7

• -120/119

• 24/7

Which quadrant is angle θ in if cos(θ) = 5/13 and θ is between 3π/2 and 2π?

• First

• Second

• Third

• Fourth

What is the exact value of 2sin(75°)cos(75°)?

• 1

• 1/2

• √2/2

• √3/2

Using the double angle formula, what is cos²(15°) - sin²(15°)?

• √2/2

• 1

• 1/2

• √3/2

What is the value of 2tan(22.5°)/(1 - tan²(22.5°))?

• √2

• √3

• 0

• 1

What is the reference angle for 150°?

• 90°

• 45°

• 30°

• 60°