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)

Tags

CCSS.HSF.TF.C.9

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

Tags

CCSS.HSF.TF.C.9

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

Tags

CCSS.HSF.TF.C.9

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

• 18/25

• -7/25

• 7/25

• -18/25

Tags

CCSS.HSF.TF.C.9

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

• -24/25

• 24/25

• -24/5

• 24/5

Tags

CCSS.HSF.TF.C.9

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

• -24/7

• 24/7

• -7/24

• 7/24

Tags

CCSS.HSF.TF.C.9

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

• Second quadrant

• Third quadrant

• First quadrant

• Fourth quadrant

Tags

CCSS.HSF.TF.C.9

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

Tags

CCSS.HSF.TF.C.9

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

Tags

CCSS.HSN.RN.A.2

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

• 1/4

• -1/4

• √2/4

• -√2/4

Tags

CCSS.HSN.RN.A.2