Trigonometric Functions and Identities

The video tutorial explains how to solve a trigonometry problem involving a given cosecant value for an angle in the second quadrant. It covers setting up a reference triangle, using the Pythagorean theorem, and applying half-angle identities to find sine, cosine, and tangent values. The tutorial also demonstrates using a calculator to approximate these values.

What is the reciprocal of the sine function?

• Secant

• Cosecant

• Tangent

• Cotangent

In which quadrant does the angle terminate if it is between 90 and 180 degrees?

• Second

• First

• Fourth

• Third

What is the length of the hypotenuse in the reference triangle if cosecant x is 4?

• 1

• 4

• 3

• 2

What is the length of the adjacent side in the reference triangle if the opposite side is 1 and the hypotenuse is 4?

• √15

• √17

• √19

• √13

In which quadrant does x/2 lie if x is between 90 and 180 degrees?

• Fourth

• Second

• First

• Third

What is the approximate value of sine(x/2) calculated using the half-angle identity?

• 0.1260

• 0.7071

• 0.9920

• 0.5000

What is the formula for cosine(x/2) using the half-angle identity?

• √(1 - sin(x))/2

• √(1 + sin(x))/2

• √(1 + cos(x))/2

• √(1 - cos(x))/2

What is the approximate value of cosine(x/2) calculated using the half-angle identity?

• 0.1260

• 0.9920

• 0.5000

• 0.7071

How is tangent(x/2) calculated using sine(x/2) and cosine(x/2)?

• sine(x/2) * cosine(x/2)

• sine(x/2) + cosine(x/2)

• sine(x/2) / cosine(x/2)

• cosine(x/2) / sine(x/2)

What is the approximate value of tangent(x/2) calculated using sine(x/2) and cosine(x/2)?

• 0.1260

• 7.8730

• 0.9920

• 1.0000