The video tutorial explains how to find the exact value of sine 105 degrees using sum and difference formulas. It begins by discussing why the unit circle and calculator approximations are insufficient for this task. The instructor then demonstrates how to rewrite 105 degrees as a sum of known angles and applies the sum formula to calculate the exact value. The tutorial concludes with a discussion on simplifying the expression and understanding radical rules.

Why can't the unit circle be used directly to find the sine of 105 degrees?

• The angle is not a standard angle on the unit circle.

• The unit circle only works for angles less than 90 degrees.

• 105 degrees is not a real angle.

• The unit circle is only for cosine values.

What is the purpose of using sum and difference formulas in this context?

• To simplify the use of a calculator.

• To convert degrees to radians.

• To find the exact value of sine 105 degrees.

• To approximate the value of sine 105 degrees.

How can 105 degrees be expressed using known angles?

• As the sum of 60 and 45 degrees.

• As the sum of 30 and 75 degrees.

• As the difference of 90 and 15 degrees.

• As the difference of 120 and 15 degrees.

What does the sum and difference formula for sine involve?

• Adding the sine values of two angles.

• Multiplying the sine and cosine values of two angles.

• Dividing the sine values of two angles.

• Subtracting the cosine values of two angles.

What is the sine of 60 degrees?

• Square root of 3 / 2

• 1/2

• Square root of 2 / 2

• 0

What is the cosine of 45 degrees?

• 1/2

• Square root of 3 / 2

• Square root of 2 / 2

• 0

Which of the following is a correct way to express the final answer for sine 105 degrees?

• Square root of 2 times (Square root of 3 + 1) / 4

• Square root of 6 + Square root of 2

• Square root of 3 / 2 + Square root of 2 / 2

• Square root of 4 + Square root of 9