Trigonometric Functions and Identities

The video tutorial explains how to use the sum and difference identity for cosine to find the exact trigonometric value of cosine 13 pi/12 radians. It begins by converting the angle from radians to degrees, resulting in 195 degrees. The tutorial then explores different angle combinations that sum or differ to 195 degrees, focusing on those with known trigonometric values. The chosen combination is 150 degrees and 45 degrees. The video demonstrates applying the identity and using reference triangles to evaluate the trigonometric functions, leading to the final result. It concludes by discussing alternative forms of the answer.

What is the main goal of using the sum and difference identity for cosine in this example?

• To convert radians to degrees

• To determine the exact value of cosine 13π/12 radians

• To find the tangent of 13π/12 radians

• To find the sine of 13π/12 radians

Tags

CCSS.HSF.TF.A.1

What is the degree equivalent of 13π/12 radians?

• 210 degrees

• 165 degrees

• 195 degrees

• 180 degrees

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CCSS.HSF.TF.A.4

Why is it important to use angles with known trigonometric values?

• They are easier to memorize

• They are always in the first quadrant

• They are only used in radians

• They simplify the calculation process

Tags

CCSS.HSF.TF.C.9

Which pair of angles can be used to express 195 degrees using known trigonometric values?

• 160 degrees + 35 degrees

• 150 degrees + 45 degrees

• 120 degrees + 75 degrees

• 180 degrees + 15 degrees

Tags

CCSS.HSF.TF.A.2

What is the cosine of 150 degrees?

• -1/2

• √2/2

• -√3/2

• 1/2

Tags

CCSS.HSF.TF.A.2

What is the sine of 45 degrees?

• √2/2

• √3/2

• 1

• 1/2

Tags

CCSS.HSF.TF.A.2

What is the significance of using reference triangles in this context?

• They help in converting degrees to radians

• They are used to find the hypotenuse

• They provide a visual aid to evaluate trigonometric functions

• They simplify the addition of angles

Tags

CCSS.HSF.TF.A.2

What is the cosine of 45 degrees?

• 1

• √2/2

• √3/2

• 1/2

Tags

CCSS.HSF.TF.C.9

What is the result of the expression for cosine 195 degrees using the sum identity?

• Negative square root of 6 plus square root of 2 divided by 4

• Square root of 6 plus square root of 2 divided by 4

• Negative square root of 6 minus square root of 2 divided by 4

• Square root of 6 minus square root of 2 divided by 4

Tags

CCSS.HSF.TF.C.9

How can the final result of the cosine calculation be expressed differently?

• By changing the denominator

• By factoring out a negative sign

• By using a different angle pair

• By converting to radians

Tags

CCSS.HSF.TF.C.9