Trigonometric Identities and Functions

The video tutorial covers double angle identities for cosine, sine, and tangent, explaining their formulas and how to verify them using sum identities. It includes example problems to find the values of cosine, sine, and tangent of 2A given certain conditions, and discusses determining the quadrant of an angle. The video concludes with a summary of the key points discussed.

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

• cos(2A) = sin^2(A) + cos^2(A)

• cos(2A) = 2cos^2(A) - 1

• cos(2A) = 1 - 2sin^2(A)

• cos(2A) = cos^2(A) - sin^2(A)

What is the double angle identity for sine?

• sin(2A) = 2sin(A)cos(A)

• sin(2A) = 2cos^2(A) - 1

• sin(2A) = 1 - 2cos^2(A)

• sin(2A) = sin^2(A) - cos^2(A)

How can the double angle identity for cosine be verified using sum identities?

• By using the identity for cos(A + A)

• By using the identity for sin(A + A)

• By using the identity for sin(A + B)

• By using the identity for tan(A + B)

If sin(A) = 3/5 in the second quadrant, what is cos(2A)?

• -18/25

• 18/25

• -7/25

• 7/25

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

• -24/5

• -24/25

• 24/25

• 24/5

What is the tangent of angle A if sin(A) = 3/5 and cos(A) = -4/5?

• -4/3

• 4/3

• -3/4

• 3/4

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

• Fourth quadrant

• Third quadrant

• Second quadrant

• First quadrant

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

• 135 to 180 degrees

• 90 to 135 degrees

• 45 to 90 degrees

• 0 to 45 degrees

What is the cosine of angle A if cos(2A) = -3/4 and angle A is in the second quadrant?

• √2/4

• 1/2√2

• -√2/4

• -1/2√2

How is the cosine of angle A rationalized if it is initially -1/2√2?

• -√2/4

• √2/4

• -2√2/4

• 2√2/4