Trigonometric Functions and Identities

The video tutorial explains how to solve a trigonometric equation involving cotangent and cosecant over a given interval. It begins with substitutions using reciprocal identities, followed by solving the equation by setting the numerator to zero. The tutorial then demonstrates finding angles with a cosine value of negative one-half using reference triangles and verifies these solutions using the unit circle. The solutions are confirmed to be correct, and the process is explained in a step-by-step manner.

What is the reciprocal identity for cotangent x?

• One divided by sine x

• One divided by cosine x

• Cosine x divided by sine x

• Sine x divided by cosine x

When is a fraction equal to zero?

• When the fraction is undefined

• When the denominator is zero

• When the numerator is zero

• When both numerator and denominator are zero

What is the cosine value of a 60-degree angle?

• One

• Zero

• One-half

• Negative one-half

In which quadrants is the cosine value negative?

• First and fourth

• Third and fourth

• First and second

• Second and third

What is 120 degrees in radians?

• Three pi

• One-third pi

• Four-thirds pi

• Two-thirds pi

What is the angle in the third quadrant with a cosine value of negative one-half?

• 300 degrees

• 240 degrees

• 180 degrees

• 120 degrees

Which of the following angles does not have a sine value of zero?

• 0 degrees

• 90 degrees

• 180 degrees

• 240 degrees

On the unit circle, what does the x-coordinate represent?

• Cosecant theta

• Tangent theta

• Cosine theta

• Sine theta

Which angle corresponds to an x-coordinate of negative one-half in the second quadrant?

• 60 degrees

• 120 degrees

• 180 degrees

• 240 degrees

What is the x-coordinate of the angle 240 degrees on the unit circle?

• One-half

• Negative one

• Negative one-half

• Zero