Pre-Calculus - How to find the exact value by using the sum of two angles formula with cosine

The video tutorial explains how to find the exact value of cosine 75 degrees, which is not directly available on the unit circle. It discusses the limitations of using a calculator for exact values and introduces the angle sum formula to rewrite 75 degrees as a sum of known angles. The tutorial walks through the application of the formula, plugging in values for cosine and sine of 30 and 45 degrees, and demonstrates how to simplify the result. It also highlights the importance of understanding the unit circle and the need for simplification in mathematical expressions.

Why is using a calculator not ideal for finding the exact value of cosine 75 degrees?

• It only works for angles in radians.

• It provides a decimal approximation.

• It gives an exact value.

• It cannot calculate cosine.

Which two angles can be used to express 75 degrees as a sum?

• 45 degrees and 60 degrees

• 30 degrees and 45 degrees

• 0 degrees and 90 degrees

• 30 degrees and 60 degrees

What is the formula for cosine of the sum of two angles?

• cos(U + V) = sin(U) * sin(V) - cos(U) * cos(V)

• cos(U + V) = sin(U) * cos(V) + cos(U) * sin(V)

• cos(U + V) = cos(U) * cos(V) - sin(U) * sin(V)

• cos(U + V) = cos(U) * cos(V) + sin(U) * sin(V)

What is the cosine of 30 degrees?

• sqrt(2)/2

• 1/2

• sqrt(3)/2

• 0

What is the sine of 45 degrees?

• sqrt(2)/2

• 1

• 1/2

• sqrt(3)/2

How can the expression sqrt(6)/4 - sqrt(2)/4 be further simplified?

• By factoring out 1/4

• By factoring out 1/2

• By factoring out sqrt(2)

• By factoring out sqrt(3)

What is a possible simplified form of the expression sqrt(6)/4 - sqrt(2)/4?

• sqrt(3)/2

• sqrt(2)/2

• sqrt(2)(sqrt(3) - 1)/4

• sqrt(3) - 1