Worksheet: Directed Angles In Standard Position

In this worksheet, we will practice identifying whether the directed angle is in standard position.

Q1:

Does the ordered pair express an angle in standard position?

• Ano
• Byes

Q2:

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

• A
• B
• C
• D
• E

Q3:

Is the angle in standard position?

• Ayes
• Bno

Q4:

Is the angle in standard position?

• Ayes
• Bno

Q5:

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

Q6:

The terminal side of in standard position intersects with the unit circle at the point with coordinates . Find the value of giving the answer to the nearest second.

• A
• B
• C
• D

Q7:

In the given figure, point is on the unit circle and lies in the interval .

From the right triangle , what ratio gives ?

• A
• B
• C
• D
• E

Which of the following is true concerning the triangles and ?

• AThey are similar.
• BThey are equilateral.
• CThey are isosceles.
• DThey are congruent.
• EThey are scalene.

What is the scale factor of to ?

• A
• B
• C
• D
• E

Use your answers to the previous parts to determine the length of in terms of and .

• A
• B
• C
• D
• E

Q8:

Consider a windmill with blades of length 1 m. The position of the top of a given blade is given by its coordinates which depend upon angle as shown.

Express and as functions of the measure of angle in radians.

• A
• B
• C
• D
• E

If the angle at a certain time is , what will it be after the blade has completed half a rotation?

• A
• B
• C
• D
• E

Q9:

In the given figure, point is on the unit circle and lies in the interval .

Is positive or negative?

• Anegative
• Bpositive

Which of the following is true concerning the triangles , and ?

• AThey are similar.
• BThey are equilateral.
• CThey are isosceles.
• DThey are congruent.
• EThey are scalene.

Q10:

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

Q11:

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

• A1
• B0
• C
• DUndefined

Q12:

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

• A1
• B0
• C
• DUndefined

Q13:

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

Q14:

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

• A and
• B and
• C and
• D and

Q15:

Is the angle in standard position?

• Ano
• Byes

Q16:

Is the angle in standard position?

• Ano
• Byes

Q17:

Is the angle in standard position?

• Ano
• Byes

Q18:

Is the angle in standard position?

• Ayes
• Bno

Q19:

Is the angle in standard position?

• Ano
• Byes