Sine and Cosine Functions Review

The video tutorial explains how to determine the sine of the sum of two angles, specifically pi over three and pi over four. It begins by introducing the formula for the sine of angle sums and emphasizes the importance of writing down the formula. The tutorial then demonstrates how to apply the formula by labeling and substituting the angles into the equation. The unit circle is used to evaluate the sine and cosine values of the angles. Finally, the tutorial covers simplifying the resulting expression by factoring out common terms, leading to the final answer.

What is the problem being solved in this video?

• Finding the tangent of pi/4

• Finding the sine of pi/2

• Finding the cosine of pi/3

• Finding the sine of the sum of pi/3 and pi/4

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

• sin(u + v) = sin(u) * sin(v) - cos(u) * cos(v)

• sin(u + v) = cos(u) * sin(v) - sin(u) * cos(v)

• sin(u + v) = sin(u) * cos(v) + cos(u) * sin(v)

• sin(u + v) = cos(u) * cos(v) - sin(u) * sin(v)

What is the next step after writing down the formula for the sine of the sum of two angles?

• Convert the angles to degrees

• Label the angles as u and v and substitute their values

• Find the derivative of the function

• Calculate the tangent of each angle

What is the sine of pi/3 according to the unit circle?

• 1/2

• Square root of 2 over 2

• Square root of 3 over 2

• 1

What is the cosine of pi/4 according to the unit circle?

• 1/2

• Square root of 2 over 2

• Square root of 3 over 2

• 1

What is the x-coordinate for the cosine of pi/3 on the unit circle?

• Square root of 2 over 2

• 1

• 1/2

• Square root of 3 over 2

What is the y-coordinate for the sine of pi/4 on the unit circle?

• Square root of 3 over 2

• 1/2

• 1

• Square root of 2 over 2

What common factor is found in the numerator during simplification?

• 4

• Square root of 2

• 1/2

• Square root of 3

What common factor is found in the denominator during simplification?

• 4

• 1/2

• Square root of 2

• Square root of 3

What is the final simplified expression for the sine of the sum of pi/3 and pi/4?

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

• Square root of 3 over 2 times (Square root of 2 + 1)

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

• Square root of 2 over 2 times (Square root of 3 + 1)