Unit Circle and Trigonometric Ratios

This lesson explores how a unit circle can be used to study angles and find the values of sine, cosine, and tangent functions. It reviews the properties of 30-60-90 and 45-45-90 triangles and explains how to use these triangles to determine trigonometric ratios on the unit circle. The lesson also provides methods for calculating and memorizing trigonometric values for special angles.

What is the significance of the smallest angle in a 30-60-90 triangle?

• It is equal to the largest angle.

• It is the hypotenuse.

• It is opposite the smallest side.

• It is opposite the largest side.

What happens to the sine and cosine ratios when using a unit circle?

• They are multiplied by the radius.

• They become undefined.

• They simplify to the coordinates x and y.

• They become equal to the radius.

In a unit circle, what is the tangent of an angle defined as?

• The difference between x and y coordinates.

• The product of x and y coordinates.

• The ratio of y to x coordinates.

• The sum of x and y coordinates.

How do you adjust a 30-60-90 triangle to fit in a unit circle?

• Divide all sides by the hypotenuse.

• Multiply all sides by the hypotenuse.

• Divide all sides by 2.

• Multiply all sides by 2.

What are the coordinates for a 45-degree angle in the unit circle?

• √3/2, 1/2

• √2/2, √2/2

• 1, 0

• 0, 1

For a 60-degree angle, what is the tangent value in the unit circle?

• 1

• 1/√3

• 0

• √3

What is the cosine of a 30-degree angle in the unit circle?

• 1/2

• √3/2

• √2/2

• 0

How can you easily remember the sine and cosine values for special angles?

• By using a protractor.

• By drawing the unit circle each time.

• By memorizing a chart with radicals and fractions.

• By using a calculator.

What is the sine of 0 degrees according to the chart method?

• 1

• 0

• √3/2

• 1/2

What is the pattern for filling in the sine column in the chart method?

• 4, 3, 2, 1, 0

• 0, 1, 2, 3, 4

• 0, 1, 3, 2, 4

• 1, 2, 3, 4, 0