Trigonometric Functions and Reference Angles

This lesson covers how to find the exact value of trigonometric functions using reference angles. It explains the concept of coterminal angles and the signs of trigonometric functions in different quadrants. The lesson details how to calculate reference angles and use them to determine trigonometric ratios. It emphasizes the importance of drawing reference triangles correctly and provides examples, such as finding the sine of 120 degrees using a reference angle of 60 degrees.

What is the main goal of this lesson?

• To evaluate trigonometric functions using reference angles

• To learn how to use a calculator for trigonometric functions

• To understand the history of trigonometry

• To memorize the unit circle

What is a coterminal angle?

• An angle that is always negative

• An angle that is always positive

• An angle that is a multiple of 90 degrees

• An angle that shares the same terminal side as another angle

In which quadrant are sine and cosecant positive?

• First quadrant

• Second quadrant

• Fourth quadrant

• Third quadrant

What is a reference angle?

• An angle that is always 180 degrees

• An acute angle formed with the x-axis

• An angle that is always 360 degrees

• An angle that is always 90 degrees

How do you find the reference angle in the second quadrant?

• Add the angle to 360 degrees

• Add the angle to 180 degrees

• Subtract the angle from 180 degrees

• Subtract the angle from 360 degrees

What is the reference angle for 460 degrees?

• 120 degrees

• 100 degrees

• 80 degrees

• 60 degrees

How do you determine if a trig ratio is positive or negative?

• By using a calculator

• By using the Pythagorean theorem

• By using a simple trig chart

• By guessing

What is the sine of 120 degrees?

• Zero

• Negative one

• Radical three over two

• 1/2

Why is it important to draw the reference triangle to the x-axis?

• To ensure the reference angle is correct

• To memorize the unit circle

• To make the drawing look better

• To avoid using a calculator

What happens if you draw the reference triangle incorrectly?

• It doesn't affect the result

• It makes the calculation faster

• It gives the wrong reference angle

• It makes the angle negative