Given an angle and constraint find the six trig functions of the angle

The video tutorial explains how to evaluate all six trigonometric functions given specific constraints. It starts by introducing the problem of finding trigonometric values when the cosecant of Theta equals four and the cotangent is less than zero. The instructor uses a triangle and the unit circle to determine the values, focusing on the relationship between sine and cosecant. The video also covers how to identify the correct quadrant for the triangle based on cotangent constraints and uses the Pythagorean theorem to find missing side lengths. Finally, it demonstrates how to evaluate each trigonometric function, including rationalizing denominators.

What is the reciprocal of the sine function?

• Tangent

• Cosecant

• Secant

• Cosine

In which quadrants is the cotangent function negative?

• First and Second

• Second and Fourth

• Third and Fourth

• First and Third

Why is the second quadrant chosen for the triangle construction?

• Because Y is negative

• Because X is positive

• Because Y is positive and cotangent is negative

• Because X and Y are both negative

What theorem is used to find the missing side of the triangle?

• Cosine Rule

• Tangent Rule

• Sine Rule

• Pythagorean Theorem

What is the value of sine Theta given the triangle's sides?

• 1/3

• 1/4

• 1/5

• 1/2

How do you rationalize the denominator for the tangent function?

• Divide by the numerator

• Multiply by the square root of the denominator

• Multiply by the conjugate

• Add a constant

What is the value of cotangent Theta in the second quadrant?

• Positive

• Undefined

• Zero

• Negative