Cosine and Angle Identities

The video tutorial explains how to find the exact value of cosine 105° using the half angle identity. It begins by determining the value of 'a' and whether the cosine function is positive or negative. The tutorial then demonstrates finding cosine 210° using a reference triangle and the unit circle. The expression is simplified, and the result is verified using a calculator. Finally, the video compares the results obtained using the half angle identity with those from the sum identity, showing that different methods yield the same value.

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

• To approximate the value of cosine 105°

• To find the exact value of tangent 105°

• To find the exact value of cosine 105°

• To find the exact value of sine 105°

Tags

CCSS.HSF.TF.C.9

What is the value of 'a' when using the half angle identity for cosine 105°?

• 210°

• 105°

• 45°

• 60°

Tags

CCSS.HSF.TF.A.2

In which quadrant does the angle 105° terminate?

• Fourth quadrant

• Third quadrant

• Second quadrant

• First quadrant

What is the reference angle for 210°?

• 90°

• 60°

• 45°

• 30°

Tags

CCSS.HSF.TF.A.2

What is the cosine of 210°?

• -1/2

• 1/2

• -√3/2

• -√3/2

What is the simplified expression for cosine 105° using the half angle identity?

• -√(2 - √3) / 2

• √(2 - √3) / 2

• -√(2 + √3) / 2

• √(2 + √3) / 2

Tags

CCSS.HSF.TF.C.9

How is the expression for cosine 105° verified?

• By using a protractor

• By using a calculator

• By using a ruler

• By using a compass

Tags

CCSS.HSF.TF.C.9

What other identity is compared with the half angle identity in the video?

• Product-to-sum identity

• Sum-to-product identity

• Sum identity

• Double angle identity

Tags

CCSS.HSF.TF.C.9

What is the result of using the sum identity for cosine 105°?

• √2 + √6 / 4

• √6 - √2 / 4

• √3 - √2 / 4

• √2 - √6 / 4

Tags

CCSS.HSF.TF.C.9

What is the main takeaway from comparing different methods to find cosine 105°?

• Different methods yield different values

• Different methods yield the same value

• Only one method is correct

• None of the methods are reliable

Tags

CCSS.HSF.TF.C.9