Evaluating Trigonometric Functions

This video tutorial explains how to evaluate the six trigonometric functions using limited information, such as knowing the sine of an angle and its quadrant. The instructor demonstrates using the unit circle and right triangle to determine the lengths of triangle sides and calculate sine, cosine, tangent, and their reciprocal functions. Key concepts include the Pythagorean theorem and the importance of understanding the signs of coordinates in different quadrants.

What are the two main tools used to evaluate trigonometric functions with limited information?

• Cosine rule and unit circle

• Right triangle and sine rule

• Unit circle and right triangle

• Unit circle and Pythagorean theorem

What is the first step in evaluating trigonometric functions with limited information?

• Draw a right triangle

• Identify the quadrant

• Calculate the hypotenuse

• Find the angle

In which quadrant is angle T located if S(T) is negative and T is in quadrant 3?

• Quadrant 1

• Quadrant 2

• Quadrant 3

• Quadrant 4

What is the first step in building a right triangle in a given quadrant?

• Identify the hypotenuse

• Draw the triangle back to the x-axis

• Determine the opposite side

• Calculate the angle

How do you find the length of the missing side in a right triangle?

• Using the Pythagorean theorem

• Using the tangent function

• Using the cosine rule

• Using the sine rule

What is the reciprocal of the sine function?

• Cosine

• Cosecant

• Tangent

• Secant

What is the opposite side length if the sine of angle T is -3/5?

• -3

• 5

• -5

• 3

What is the hypotenuse length if the sine of angle T is -3/5?

• 3

• -5

• 4

• 5

What is the cosecant of angle T if S(T) is -3/5?

• -5/3

• 3/5

• 5/3

• -3/5

How is the cosine of angle T determined using a right triangle?

• Opposite over hypotenuse

• Adjacent over hypotenuse

• Hypotenuse over adjacent

• Hypotenuse over opposite