Cosine Function Value of 105 Degrees

The video tutorial demonstrates how to find the exact value of cosine 105 degrees using a half angle identity and a power reducing identity. It explains the process of applying these identities, calculating cosine 210 degrees using a reference triangle, and simplifying the expression to find the final result. The tutorial also discusses determining the sign of the cosine value based on the quadrant in which the angle lies.

What mathematical identity is used to find the cosine of 105 degrees in this video?

• Double angle identity

• Half-angle identity

• Product-to-sum identity

• Sum of angles identity

What is the expression for cosine squared 'a' using the power-reducing identity?

• 1/2(1 - cos(2a))

• 1/2(1 + cos(2a))

• 1 + sin(2a)

• 1 - sin^2(a)

In which quadrant is the angle 210 degrees located?

• Fourth quadrant

• Third quadrant

• Second quadrant

• First quadrant

What is the cosine of 210 degrees?

• 1/2

• -1/2

• √3/2

• -√3/2

What operation is performed to eliminate the denominator in the expression for cosine squared 105 degrees?

• Multiplication

• Subtraction

• Addition

• Division

What must be considered when taking the square root of both sides of an equation?

• Neither root

• Both positive and negative roots

• Only the negative root

• Only the positive root

In which quadrant is the angle 105 degrees located?

• Fourth quadrant

• Second quadrant

• Third quadrant

• First quadrant

What is the sign of the cosine function in the second quadrant?

• Positive

• Undefined

• Negative

• Zero

What is the exact value of cosine 105 degrees?

• √(2 + √3) / 2

• √2 - √3 / 2

• -√2 + √3 / 2

• -√(2 - √3) / 2

Why is it important to determine the sign of the cosine function value?

• To ensure the angle is in the correct quadrant

• To confirm the angle is obtuse

• To check if the angle is reflex

• To verify the angle is acute