Understanding Cosine Using Half Angle Identity

The video tutorial demonstrates how to determine the exact value of cosine 5 pi/12 radians using a half angle identity. It begins by converting the angle from radians to degrees, then identifies the angle 'A' needed for the identity. The tutorial explains how to determine the sign of the function value and applies the half angle identity. It calculates the cosine of 150 degrees and simplifies the expression to find the exact value.

What is the first step in finding the exact value of cosine 5π/12 radians?

• Find the sine of the angle

• Apply the Pythagorean identity

• Convert the angle to degrees

• Use the double angle formula

What is the degree equivalent of 5π/12 radians?

• 90 degrees

• 75 degrees

• 120 degrees

• 60 degrees

In the half-angle identity for cosine, what is the relationship between angle 'A' and the given angle?

• 'A' is the square of the given angle

• 'A' is double the given angle

• 'A' is the same as the given angle

• 'A' is half the given angle

Why is the cosine of 75 degrees positive?

• Because it is in the second quadrant

• Because cosine is always positive

• Because it is in the first quadrant

• Because it is in the third quadrant

What is the reference angle used to find cosine 150 degrees?

• 90 degrees

• 60 degrees

• 30 degrees

• 45 degrees

In which quadrant is the angle 150 degrees located?

• First quadrant

• Second quadrant

• Third quadrant

• Fourth quadrant

What is the cosine of 150 degrees?

• -√3/2

• 1/2

• -1/2

• √3/2

What operation is performed to clear the denominator in the expression?

• Multiplication

• Addition

• Subtraction

• Division

What is the simplified denominator under the square root?

• 3

• 4

• 2

• 1

What is the final exact value of cosine 5π/12 radians?

• √3/2

• 1/2

• √2/2

• √6/4