Trigonometric Identities and Formulas

The video tutorial covers double angle formulas for sine and cosine, explaining their derivations and applications. It provides multiple forms of the cosine double angle formula and demonstrates their use through example problems. The tutorial emphasizes understanding the formulas and applying them to solve trigonometric problems without relying on calculators.

What is the formula for the sine of a double angle?

• sin(2θ) = 2cos^2(θ) - 1

• sin(2θ) = 1 - 2sin^2(θ)

• sin(2θ) = 2sin(θ)cos(θ)

• sin(2θ) = sin^2(θ) - cos^2(θ)

Which of the following is NOT a formula for the cosine of a double angle?

• cos(2θ) = 2cos^2(θ) - 1

• cos(2θ) = 2sin(θ)cos(θ)

• cos(2θ) = cos^2(θ) - sin^2(θ)

• cos(2θ) = 1 - 2sin^2(θ)

If cos(x) = 3/4, what is the first step to find sin(2x)?

• Assume sin(x) = 1 - cos(x)

• Use the identity sin^2(x) + cos^2(x) = 1

• Use the formula cos(2x) = 2cos^2(x) - 1

• Directly calculate sin(2x) using 2sin(x)cos(x)

What identity is used to find sin(x) from cos(x)?

• sin(2x) = 2sin(x)cos(x)

• cos(2x) = cos^2(x) - sin^2(x)

• tan(x) = sin(x)/cos(x)

• sin^2(x) + cos^2(x) = 1

Why is the positive value of sin(x) chosen when x is an acute angle?

• Because cos(x) is negative

• Because acute angles are in the first quadrant where sine is positive

• Because it simplifies calculations

• Because sin(x) is always positive

In the example with s(α) = 3/5 and cos(α) = -4/5, what is the formula used to find s(2α)?

• s(2α) = 2cos^2(α) - 1

• s(2α) = 2sin(α)cos(α)

• s(2α) = sin^2(α) - cos^2(α)

• s(2α) = 1 - 2sin^2(α)

Which formula is used to find cos(2α) in the example problem?

• cos(2α) = cos^2(α) - sin^2(α)

• cos(2α) = 2cos^2(α) - 1

• cos(2α) = 1 - 2sin^2(α)

• cos(2α) = 2sin(α)cos(α)