Evaluating for sine using the half angle formula

The video tutorial explains how to find the sine of 105 degrees using the half angle formula. It begins by discussing the limitations of using the unit circle and sum and difference formulas for this angle. The instructor introduces the half angle formula and demonstrates its application to solve for sine of 105 degrees. The process involves algebraic simplification and understanding the properties of trigonometric functions in different quadrants. The tutorial concludes with the final simplified expression for the sine of 105 degrees.

Why is the sine of 105 degrees not directly available on the unit circle?

• Because the unit circle only includes angles in radians.

• Because 105 degrees is not a standard angle on the unit circle.

• Because the unit circle only includes angles up to 90 degrees.

• Because 105 degrees is a negative angle.

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

• To calculate the area of a triangle.

• To find the tangent of an angle.

• To break down complex angles into simpler ones.

• To convert angles into radians.

What does the half-angle formula help to determine?

• The sine of an angle divided by two.

• The cosine of an angle multiplied by two.

• The tangent of an angle divided by two.

• The cotangent of an angle multiplied by two.

In which quadrant is the angle 105 degrees located?

• Fourth quadrant

• Second quadrant

• First quadrant

• Third quadrant

What is the cosine of 210 degrees?

• -1/2

• 1/2

• -sqrt(3)/2

• sqrt(3)/2

How do you simplify a fraction divided by another number?

• Divide the numerator and denominator by the same number.

• Subtract the same number from both the numerator and denominator.

• Add the same number to both the numerator and denominator.

• Multiply the numerator and denominator by the same number.

What is the final simplified form of the expression for sine 105 degrees?

• sqrt(2) - sqrt(3)/2

• sqrt(2) + sqrt(3)/2

• 2 - sqrt(3)/2

• 2 + sqrt(3)/2