# Lesson Worksheet: Trigonometric Ratios on the Unit Circle Mathematics • 10th Grade

In this worksheet, we will practice relating the 𝑥- and 𝑦-coordinates of points on the unit circle to trigonometric functions.

Q1:

Find the value of .

Q2:

In the figure, points and lie on the unit circle, and . Express the values of sine, cosine, and tangent of in terms of their values for . Check whether this is valid for all values of .

• A
• B
• C
• D
• E

Q3:

Find , given is in standard position and its terminal side passes through the point .

• A
• B
• C
• D

Q4:

Find , given is in standard position and its terminal side passes through the point .

• A
• B
• C
• D

Q5:

Find given is in standard position and its terminal side passes through the point .

• A
• B
• C
• D

Q6:

The terminal side of in standard position intersects with the unit circle at the point with coordinates where is a postive number. Find .

• A
• B1
• C
• D

Q7:

The terminal side of in standard position intersects the unit circle at the point with coordinates , where . Find the value of .

• A
• B
• C
• D

Q8:

Suppose is a point on a unit circle corresponding to the angle of . Is there another point on the unit circle representing an angle in the interval that has the same tangent value? If yes, give the angle.

• AYes,
• BNo
• CYes,
• DYes,
• EYes,

Q9:

Consider , a point on a unit circle corresponding to the angle of . Is there another point on the unit circle that has the same -coordinate as and represents an angle in the interval ? If yes, give the angle.

• AYes,
• BYes,
• CYes,
• DNo
• EYes,

Q10:

Find the equation of the straight line that makes an angle of , measured in radians, with the positive direction of the -axis in the standard position in the unit circle.

• A
• B
• C
• D