# Worksheet: Trigonometric Functions of Standard Position Angle

In this worksheet, we will practice finding the values of the six trigonometric functions of an angle θ given in standard position.

Q1:

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

• A
• B
• C
• D

Q2:

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

Q3:

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

• A
• B
• C
• D

Q4:

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

• A
• B
• C
• D

Q5:

Two points and lie on the unit circle centered at the origin such that the coordinate of are and . Which of the following properties of do you need to use to find the coordinates of point .

• AAll three internal angles are equal.
• BThe height of an equilateral triangle is half its median.
• CThe height of an equilateral triangle is equal to its side.
• DThe height of an equilateral triangle is also its median.
• EAll three sides are equal.

Hence, find and .

• A
• B
• C
• D
• E

The line intersects the line at . The triangle is formed by reflecting in the line . What kind of triangle is the triangle ?

• AIsosceles
• BEquilateral
• CRight
• DScalene

Find (i.e., ).

• A
• B1
• C
• D
• E

Q6:

Find the value of where is the measure of an angle in standard position whose terminal side passes through .

Q7:

Find the value of where is the measure of an angle in standard position whose terminal side passes through .

Q8:

Find the value of where is the measure of an angle in standard position whose terminal side passes through .

Q9:

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

• A
• B
• C
• D

Q10:

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

• A
• B
• C
• D

Q11:

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

• A
• B
• C
• D

Q12:

The terminal side of the angle intersects the unit circle at the point where is a positive acute angle drawn in standard position. Find the value of .

• A
• B
• C
• D

Q13:

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

• A
• B
• C
• D

Q14:

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

• A
• B
• C
• D

Q15:

The terminal side of the angle intersects the unit circle at the point where is a positive acute angle drawn in standard position. Find the value of giving the answer to the nearest second.

• A
• B
• C
• D

Q16:

If the angle is in the standard position, , and , is it possible for to measure ?

• AYes
• BNo

Q17:

The terminal side of intersects the unit circle at the point where . Find the exact value of .

• A
• B
• C
• D

Q18:

The terminal side of intersects the unit circle at the point where . Find the value giving the answer to the nearest second.

• A
• B
• C
• D

Q19:

Find the value of where is the measure of an angle in standard position whose terminal side passes through .

Q20:

Find the value of where is the measure of an angle in standard position whose terminal side passes through .

• AUndefined
• B1
• C0
• D

Q21:

Find the value of where is the measure of an angle in standard position whose terminal side passes through .

• A
• B0
• CUndefined
• D1