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

**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