Understanding Trigonometric Expressions

The video tutorial explains how to find the exact value of the expression sine of two times the inverse cosine of negative three-fifths. It begins by identifying the angle theta, whose cosine value is negative three-fifths, and models it on the coordinate plane. The reference triangle is sketched, and the Pythagorean theorem is used to find the length of the opposite side. Finally, the double angle identity for sine is applied to evaluate sine two theta, resulting in the expression's value of negative 24/25.

What is the initial expression we are asked to evaluate?

• Sine of inverse cosine of negative three-fifths

• Sine of two times inverse cosine of negative three-fifths

• Cosine of two times inverse sine of negative three-fifths

• Tangent of inverse sine of negative three-fifths

Tags

CCSS.HSF.TF.A.2

In which quadrant is the angle theta located?

• First quadrant

• Second quadrant

• Third quadrant

• Fourth quadrant

Tags

CCSS.HSG.SRT.C.6

What is the ratio of the adjacent side to the hypotenuse for angle theta?

• Negative three-fifths

• Negative four-fifths

• Four-fifths

• Three-fifths

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

What theorem is used to find the length of the opposite side of the triangle?

• Sine rule

• Tangent rule

• Cosine rule

• Pythagorean theorem

Tags

CCSS.4.MD.A.1

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

• 6 units

• 5 units

• 4 units

• 3 units

Tags

CCSS.8.EE.A.2

What is the value of a squared after simplifying the equation?

• 36

• 25

• 16

• 9

Tags

CCSS.HSF.TF.C.9

What is the double angle identity for sine used in this problem?

• Sine 2a = 2 Cosine a Sine a

• Sine 2a = 2 Sine a Cosine a

• Sine 2a = Sine a + Cosine a

• Sine 2a = Sine a - Cosine a

Tags

CCSS.HSF.TF.C.8

What is the final value of the expression sine 2 theta?

• -24/5

• -24/25

• 24/25

• 24/5

Tags

CCSS.HSF.TF.C.8

What is the value of sine theta in the reference triangle?

• 3/5

• 4/5

• -3/5

• -4/5

Tags

CCSS.HSF.TF.A.2

What is the value of cosine theta in the reference triangle?

• -3/5

• -4/5

• 3/5

• 4/5

Tags

CCSS.HSF.TF.A.2