Trigonometric Identities and Calculations

The video tutorial explains how to determine the sine, cosine, and tangent of 2 theta given that cosine theta equals -5/13 and theta is in the second quadrant. It involves creating a reference triangle to find the necessary trigonometric values and applying double angle identities to calculate the desired results. The tutorial also demonstrates the use of different identities and shortcuts to find these values efficiently.

What is the given value of cosine theta in the problem?

• -5/13

• 5/13

• -12/13

• 12/13

Tags

CCSS.HSF.TF.A.2

In which quadrant is angle theta located?

• Quadrant 3

• Quadrant 4

• Quadrant 1

• Quadrant 2

Tags

CCSS.HSF.TF.A.2

What is the length of the opposite side in the reference triangle?

• 5

• 12

• 13

• 10

Tags

CCSS.HSF.TF.C.8

What is the value of sine theta based on the reference triangle?

• 5/13

• -12/13

• 12/13

• -5/13

Tags

CCSS.HSF.TF.C.8

How is sine of 2 theta calculated using the double angle identity?

• 2 * cosine theta * sine theta

• sine theta - cosine theta

• sine theta + cosine theta

• 2 * sine theta * cosine theta

Tags

CCSS.HSF.TF.C.9

What is the calculated value of sine 2 theta?

• 120/169

• -120/169

• 119/169

• -119/169

Tags

CCSS.HSF.TF.C.9

Which identity is used to calculate cosine of 2 theta?

• cosine theta + sine theta

• 2 * cosine theta * sine theta

• sine squared theta + cosine squared theta

• cosine squared theta - sine squared theta

Tags

CCSS.HSF.TF.C.9

What is the calculated value of cosine 2 theta?

• -119/169

• 119/169

• 120/169

• -120/169

Tags

CCSS.HSF.TF.C.9

How is tangent of 2 theta calculated using sine and cosine of 2 theta?

• sine 2 theta / cosine 2 theta

• cosine 2 theta / sine 2 theta

• cosine theta / sine theta

• sine theta / cosine theta

Tags

CCSS.HSF.TF.C.9

What is the final value of tangent 2 theta?

• 120/119

• -120/119

• 119/120

• -119/120

Tags

CCSS.HSF.TF.C.9