Pre-Calculus - How to Evaluate Using The Double Angle of Sine

The video tutorial explains how to solve a trigonometry problem involving the sine of a double angle. It begins by setting up the problem and identifying constraints, which help in selecting the correct triangle in the third quadrant. The tutorial then uses the double angle formula for sine and applies the Pythagorean theorem to find the missing side of the triangle. Finally, it calculates the sine of the double angle, resulting in a positive value.

What is the relationship between sine and the hypotenuse in a right triangle?

• Sine is the ratio of the hypotenuse to the opposite side.

• Sine is the ratio of the adjacent side to the opposite side.

• Sine is the ratio of the opposite side to the hypotenuse.

• Sine is the ratio of the hypotenuse to the adjacent side.

In which quadrant is the triangle located if the angle is between π and 3π/2?

• First quadrant

• Fourth quadrant

• Second quadrant

• Third quadrant

What formula is used to find the sine of a double angle?

• Sine of 2U = 2 sine U + cosine U

• Sine of 2U = sine U / cosine U

• Sine of 2U = sine U * cosine U

• Sine of 2U = 2 sine U * cosine U

How do you determine the adjacent side in a right triangle when given the opposite side and hypotenuse?

• Use the sine formula

• Use the cosine formula

• Use the Pythagorean theorem

• Use the tangent formula

What is the final result for the sine of the double angle in this problem?

• 24/25

• 12/25

• 6/25

• 18/25