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In this lesson, we will learn how to identify whether the directed angle is in standard position.

Q1:

The terminal side of angle π in standard position intersects with the unit circle at the point, ( 2 π , 3 π ) where 0 < π < π 2 . Find the value of π .

Q2:

The terminal side of π intersects the unit circle at the point ( β 2 0 π₯ , β 5 π₯ ) where π₯ > 0 . Find the value π giving the answer to the nearest second.

Q3:

Is the angle in standard position?

Q4:

Q5:

Q6:

Q7:

Q8:

Q9:

Q10:

Find the value of c o t π where π is the measure of an angle in standard position whose terminal side passes through ( 0 , β 6 ) .

Q11:

The terminal side of β π΄ π π΅ in standard position intersects the unit circle π at the point π΅ with coordinates οΏ 3 β 1 0 , π¦ ο , where π¦ > 0 . Find the value of s i n π΄ π π΅ .

Q12:

The terminal side of β π intersects the unit circle at the point οΌ 8 1 7 , π¦ ο where π¦ > 0 . Find the value of β π giving the answer to the nearest second and the value of π¦ as a fraction.

Q13:

Does the ordered pair express an angle in standard position?

Q14:

The terminal side of π in standard position intersects with the unit circle at the point π΅ with coordinates οΌ β 4 5 , β 3 5 ο . Find the value of π giving the answer to the nearest second.

Q15:

Find the value of s e c π where π is the measure of an angle in standard position whose terminal side passes through ( 0 , β 7 ) .

Q16:

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

From the right triangle , what ratio gives ?

Which of the following is true concerning the triangles and ?

What is the scale factor of to ?

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

Q17:

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

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

If the angle π at a certain time is 5 π 3 , what will it be after the blade has completed half a rotation?

Q18:

Is positive or negative?

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

Q19:

Find the value of c s c π where π is the measure of an angle in standard position whose terminal side passes through ( β 2 , 0 ) .

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