Unit Circle and Sine Functions

The video tutorial explains how to solve for the sine of 165 degrees using the unit circle and the formula for the sine of the subtraction of two angles. It covers the importance of choosing angles that can be evaluated on the unit circle, demonstrates how to plug values into the formula, and evaluates sine and cosine using unit circle coordinates. The tutorial concludes with the final calculation and simplification of the expression.

What is the approximate value of sine of 165 degrees?

• 0.8660

• 0.2588

• 0.5

• 0.7071

Why can't we use angles like 170 and 5 degrees for subtraction?

• They are not prime numbers.

• They are not multiples of 30.

• They are not on the unit circle.

• They are too large.

What is the formula for sine of the subtraction of two angles?

• sine(u) + sine(v)

• cosine(u) * cosine(v) - sine(u) * sine(v)

• sine(u) * cosine(v) - cosine(u) * sine(v)

• sine(u) * sine(v) + cosine(u) * cosine(v)

What is the coordinate point for 210 degrees on the unit circle?

• (-√3/2, -1/2)

• (1/2, √3/2)

• (-1/2, √3/2)

• (√2/2, √2/2)

What does the sine of an angle represent on the unit circle?

• The angle in radians

• The x-coordinate

• The y-coordinate

• The radius

What is the result of multiplying negative 1 by the square root of 2?

• 2

• Negative 2

• Square root of 2

• Negative square root of 2

What is the common factor of square root of 6 and square root of 2?

• Square root of 2

• 2

• 3

• Square root of 3

What is the final simplified expression for the problem?

• Square root of 2 over 2

• Square root of 3 over 4 times negative 1 plus square root of 2 over 4

• Square root of 2 over 4 times negative 1 plus square root of 3 over 4

• Square root of 6 over 4

What is the importance of factoring in the final step?

• To check the unit circle

• To find the angle

• To convert to radians

• To simplify the expression

What mistake was corrected in the final explanation?

• The angle was miscalculated

• The unit circle was not used

• Square root of 2 was incorrectly factored

• Square root of 3 was incorrectly factored