Double Angle Identities and Applications

This video tutorial covers double angle identities for cosine, sine, and tangent. It explains how to verify these identities using sum identities and provides example problems to find trigonometric values and determine the quadrant of angle 2a. Additionally, it demonstrates how to find the cosine of angle a given cosine 2a and quadrant information.

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

• cos(2a) = cos^2(a) - sin^2(a)

• cos(2a) = 1 - 2sin^2(a)

• cos(2a) = 2cos^2(a) - 1

• cos(2a) = sin^2(a) + cos^2(a)

What is the double angle identity for sine?

• sin(2a) = sin^2(a) - cos^2(a)

• sin(2a) = 2sin(a)cos(a)

• sin(2a) = 1 - 2cos^2(a)

• sin(2a) = 2cos^2(a) - 1

How can the identity for cos(2a) be derived using sum identities?

• By using tan(a + b) and setting b = a

• By using sin(a + b) and setting b = a

• By using sin(a)cos(b) and setting b = a

• By using cos(a + b) and setting b = a

What is the value of cos(2a) if sin(a) = 3/5 in the second quadrant?

• 18/25

• -7/25

• 7/25

• -18/25

If sin(a) = 3/5 in the second quadrant, what is the value of sin(2a)?

• -24/25

• 24/25

• -24/5

• 24/5

What is the value of tan(2a) if tan(a) = -3/4?

• -24/7

• 24/7

• -7/24

• 7/24

In which quadrant does angle 2a lie if cos(2a) is positive?

• Second quadrant

• Third quadrant

• First quadrant

• Fourth quadrant

If cos(2a) = -3/4 and 2a is in the third quadrant, what is the range of angle a?

• 45 to 90 degrees

• 90 to 135 degrees

• 135 to 180 degrees

• 0 to 45 degrees

What is the value of cos(a) if cos(2a) = -3/4 and 2a is in the third quadrant?

• -1/2√2

• 1/2√2

• √2/4

• -√2/4

How do you rationalize the expression -1/(2√2)?

• 1/4

• -1/4

• √2/4

• -√2/4