Trigonometric Functions and Identities

The video tutorial explains how to find the exact value of the expression involving cosine of two times the inverse sine of negative 12/13. It begins by modeling the angle theta on the coordinate plane and sketching the reference triangle. The Pythagorean theorem is used to find the length of the adjacent side. Finally, the double angle identity is applied to evaluate cosine two theta, resulting in the expression's value of negative 119/169.

What is the main goal of the problem discussed in the video?

• To find the sine of an angle

• To determine the cosine of two times an inverse sine value

• To calculate the tangent of an angle

• To solve a quadratic equation

Tags

CCSS.HSF.TF.A.2

In which quadrant does the angle theta terminate?

• First quadrant

• Second quadrant

• Third quadrant

• Fourth quadrant

Tags

CCSS.HSF.TF.C.8

What is the sine value of angle theta?

• 5/13

• 12/13

• -5/13

• -12/13

Tags

CCSS.8.G.B.7

What is the length of the hypotenuse in the reference triangle?

• 10

• 13

• 12

• 5

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Which theorem is used to find the length of the adjacent side?

• Pythagorean theorem

• Tangent rule

• Sine rule

• Cosine rule

Tags

CCSS.HSG.SRT.C.8

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

• 10

• 12

• 5

• 13

Tags

CCSS.HSF.TF.C.8

Which identity is used to evaluate cosine two theta?

• Tangent double angle identity

• Secant double angle identity

• Cosine double angle identity

• Sine double angle identity

Tags

CCSS.HSF.TF.C.8

What is the cosine value of theta?

• -12/13

• 12/13

• -5/13

• 5/13

Tags

CCSS.HSF.TF.C.8

What is the final value of the expression cosine two theta?

• 119/169

• -144/169

• -119/169

• 144/169

Tags

CCSS.HSF.TF.C.8

What is the square of the sine value of theta?

• 12/169

• 25/169

• 144/169

• 119/169

Tags

CCSS.HSF.TF.C.8