Using a Unit Circle to Find Trigonometric Function Values

This lesson covers finding the values of sine, cosine, and tangent using a unit circle. It reviews the 30-60-90 and 45-45-90 triangles, explaining how to use them to determine trigonometric ratios. The unit circle is introduced, showing how it simplifies the calculation of these ratios. Special triangles are applied to the unit circle to find coordinates, and methods for calculating sine, cosine, and tangent for specific angles are demonstrated. Finally, a technique for memorizing trigonometric values is provided.

What is the correct side ratio for a 30-60-90 triangle?

• 1:√2:2

• 1:1:√2

• 1:√3:2

• 1:2:√3

In a unit circle, what do the x and y coordinates represent?

• The secant and cosecant values

• The radius and diameter

• The tangent and cotangent values

• The sine and cosine values

How do you find the tangent of an angle using the unit circle?

• By dividing y by x

• By multiplying x and y

• By dividing x by y

• By adding x and y

What are the coordinates for a 30-degree angle in the unit circle?

• (1, 0)

• (√2/2, √2/2)

• (√3/2, 1/2)

• (1/2, √3/2)

For a 45-degree angle, what is the value of the tangent?

• √3/3

• 1

• √3

• 0

What is the cosine of a 60-degree angle?

• 0

• √2/2

• √3/2

• 1/2

Which method helps in memorizing sine and cosine values of special angles?

• Writing down all angles

• Creating a chart with radicals

• Drawing a large unit circle

• Using a calculator