Reference Angles and Trigonometric Functions

This video tutorial explains how to use reference angles to determine the exact value of trigonometric functions. It covers the definition of reference angles, how to find them for given angles, and the impact of quadrants on the signs of trigonometric functions. The tutorial includes example problems for secant of 225° and tangent of -3π/4, demonstrating the process of determining quadrants, reference angles, and evaluating the expressions.

What is a reference angle?

• An angle that is always negative

• A positive acute angle formed by the terminal side of a given angle and the x-axis

• An angle that is always greater than 180°

• An angle that is always less than 90°

What is the purpose of a reference angle?

• To find the exact value of a trigonometric function for an acute angle

• To convert an angle from degrees to radians

• To find the exact value of a trigonometric function for a non-acute angle

• To determine the quadrant of an angle

How do you find a reference angle for a positive angle?

• Multiply the angle by π

• Determine the quadrant and use the appropriate formula

• Add 180° to the angle

• Subtract the angle from 360°

What should you do if the angle is negative?

• Reverse the order of formulas and take the absolute value

• Subtract 180° from the angle

• Multiply the angle by -1

• Add 360° to the angle

What is the reference angle for -300°?

• 120°

• 300°

• 60°

• 240°

Which trigonometric functions are positive in the first quadrant?

• All trigonometric functions

• Cosine and secant

• Tangent and cotangent

• Sine and cosecant

In which quadrant are sine and cosecant positive?

• Quadrant 2

• Quadrant 4

• Quadrant 1

• Quadrant 3

Which trigonometric functions are positive in the third quadrant?

• All trigonometric functions

• Tangent and cotangent

• Sine and cosecant

• Cosine and secant

What is the reference angle for 225°?

• 60°

• 45°

• 90°

• 30°

In which quadrant is the angle 225° located?

• Quadrant 1

• Quadrant 2

• Quadrant 4

• Quadrant 3