Trigonometric Functions and Identities

The video tutorial covers the evaluation of double angle formulas for sine, cosine, and tangent. It begins with an introduction to the properties of double angle formulas, followed by detailed steps to evaluate each trigonometric function using these formulas. The tutorial also demonstrates the use of triangles to simplify the evaluation process and discusses the significance of quadrants in determining the signs of trigonometric values.

What is the correct formula for the sine of a double angle?

• sin(2U) = 2sin(U) + 2cos(U)

• sin(2U) = sin(U) + cos(U)

• sin(2U) = sin^2(U) - cos^2(U)

• sin(2U) = 2sin(U)cos(U)

In which quadrant is the angle 2pi/3 located, and what is the cosine value?

• Quadrant I, 1/2

• Quadrant II, -1/2

• Quadrant III, -1/2

• Quadrant IV, 1/2

Which formula can be used to find the cosine of a double angle?

• cos(2U) = 1 - 2sin^2(U)

• cos(2U) = sin^2(U) + cos^2(U)

• cos(2U) = cos^2(U) - sin^2(U)

• cos(2U) = 2cos(U)sin(U)

What is the tangent of pi/3 using the double angle formula?

• sqrt(3)

• 1

• sqrt(3)/3

• 1/2

What is the relationship between the tangent of a double angle and the tangent of the original angle?

• tan(2U) = 2tan(U) + tan^2(U)

• tan(2U) = tan(U) + 1

• tan(2U) = 2tan(U)/(1 - tan^2(U))

• tan(2U) = tan^2(U) - 1

If sine is positive and cosine is negative, in which quadrant is the angle located?

• Quadrant II

• Quadrant I

• Quadrant IV

• Quadrant III

What is the sine of a double angle if sine X is 3/5 in Quadrant II?

• -24/25

• 24/25

• -7/25

• 7/25

How do you find the third side of a triangle using the Pythagorean theorem?

• Divide the hypotenuse by one of the sides

• Multiply the two known sides

• Subtract the square of one side from the square of the hypotenuse

• Add the squares of the two known sides

What is the secant of an angle if the hypotenuse is 7 and the adjacent side is -2?

• -7/2

• 7/2

• -2/7

• 2/7

If an angle is in Quadrant IV, what are the signs of sine and cosine?

• Sine is negative, cosine is positive

• Both are positive

• Sine is positive, cosine is negative

• Both are negative