Trigonometric Functions and Identities

The video tutorial explains how to evaluate a trigonometric expression involving the sine of two times the arc cosine of negative one-third. It begins by discussing the properties of the arc cosine function and modeling the angle on the coordinate plane. The tutorial then applies the double angle identity for sine and uses a reference triangle to calculate the sine and cosine values. Finally, it evaluates the expression to find the result.

What is the main challenge in evaluating the sine of two times the arc cosine of negative one-third?

• The cosine value is positive.

• The angle is in the first quadrant.

• The coefficient of two in the inner function.

• The angle is in the third quadrant.

Tags

CCSS.HSF-BF.B.4D

What is the range of the arc cosine function?

• 0 to 90 degrees

• 0 to 270 degrees

• 0 to 180 degrees

• 0 to 360 degrees

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CCSS.HSF.TF.A.2

In which quadrant does the angle terminate if the cosine value is negative?

• Second quadrant

• First quadrant

• Third quadrant

• Fourth quadrant

Tags

CCSS.HSF.TF.A.2

What is the adjacent side length in the reference triangle if the cosine of the angle is negative one-third?

• Positive one

• Positive three

• Negative three

• Negative one

Tags

CCSS.HSF.TF.C.9

Which identity is used to evaluate sine of two theta?

• Sum of angles identity

• Double angle identity

• Pythagorean identity

• Half angle identity

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CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

What theorem is used to find the missing side of the triangle?

• Tangent rule

• Cosine rule

• Sine rule

• Pythagorean theorem

Tags

CCSS.8.EE.A.2

What is the value of y, the missing side, in terms of square roots?

• 3 square root of 2

• Square root of 8

• 2 square root of 2

• Square root of 2

Tags

CCSS.HSF.TF.A.2

What is the sine of theta in the reference triangle?

• 1/3

• Square root of 2 over 3

• 2/3

• 2 square root of 2 over 3

Tags

CCSS.HSF.TF.C.9

What is the final result of the expression sine of two times arc cosine of negative one-third?

• Two square root of two over nine

• Negative four square root of two over nine

• Four square root of two over nine

• Negative two square root of two over nine

Tags

CCSS.8.EE.A.2

Why is only the principal square root considered when finding y?

• Because y is always negative.

• Because y is negative in the second quadrant.

• Because y must be positive in the second quadrant.

• Because y is always positive.

Tags

CCSS.8.EE.A.2