Understanding Tangent PI/8 Using Half Angle Identity

The video tutorial demonstrates how to determine the exact value of tangent PI/8 using a half angle identity. It begins by converting PI/8 from radians to degrees, simplifying the expression, and applying the half angle identity. The tutorial explains the trigonometric values of 45 degrees and shows how to simplify the expression by rationalizing the denominator, ultimately finding that the exact value of tangent PI/8 is square root 2 minus 1.

What is the purpose of using a half-angle identity in this example?

• To find the exact value of tangent PI/8

• To convert degrees to radians

• To simplify the expression for sine

• To calculate the cosine of an angle

Why does the instructor prefer to convert the angle to degrees?

• Because it simplifies the application of identities

• Because the identity is only valid in degrees

• Because radians are not used in trigonometry

• Because degrees are easier to visualize

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CCSS.HSF.TF.A.1

What is the degree equivalent of PI/8 radians?

• 45 degrees

• 15 degrees

• 22.5 degrees

• 90 degrees

Tags

CCSS.HSF.TF.C.9

What is the value of angle 'A' used in the identity?

• 90 degrees

• 45 degrees

• 30 degrees

• 22.5 degrees

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CCSS.HSG.SRT.C.7

Which triangle is used to find the sine and cosine of 45 degrees?

• Scalene triangle

• Equilateral triangle

• 45-45-90 triangle

• 30-60-90 triangle

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CCSS.HSF.TF.A.2

What is the sine of 45 degrees?

• 1

• 1/2

• 1/square root 2

• Square root 2

Tags

CCSS.HSF.TF.C.9

What is the first step in simplifying the expression for tangent PI/8?

• Subtract 1 from the denominator

• Multiply by square root 2

• Add 1 to the numerator

• Multiply numerator and denominator by 2

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CCSS.HSN.RN.A.2

What is the purpose of rationalizing the denominator?

• To change the angle measurement

• To add a square root to the numerator

• To eliminate the square root from the denominator

• To make the expression more complex

Tags

CCSS.HSF.TF.C.9

What is the final simplified expression for tangent PI/8?

• Square root 2 + 1

• 1 + square root 2

• Square root 2 - 1

• 1 - square root 2

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CCSS.HSA.APR.D.6

What is the significance of dividing by a monomial in the final step?

• It adds complexity to the expression

• It allows breaking into individual fractions

• It changes the angle measurement

• It simplifies the numerator

Tags

CCSS.HSA.APR.D.6