7.7 Trig Functions of Real Numbers

Ex 1) Find the rectangular coordinates of P(t)

a. P(0) b. c. 3

4 2P P

(1, 0)

P(t) = (x, y) on unit circle

(0, –1)

x

y

angle in radianscos t sin t

(x, y)

t

2 2,

2 2

Ex 2) Determine which quadrant contains the given point P(t).

13

5P

a.

5

5

π 10

5

15

5

12.5

5

Q II

b. P(12)

π 2π3.14 ≈ ≈ 6.28

3π9.42 ≈ 4π ≈ 12.56

Q IV

radians

Try one on your whiteboard!

Write your own non-standard angle so that the point P(your angle in radians) is in Quadrant III.

(like the ones we just did in Example 2)

Then, give your angle to a partner so that they can confirm that it is in Quadrant III.

Remember that each point (x, y) on the unit circle is (cos t, sin t)

1sin csc

1cos sec

tan cot

t y ty

t x tx

y xt tx y

(since r = 1 on the unit circle)

22

2

2cos 2cos 1 cos

3 3 3

1 12 1

2 2

1 12 1

2 41 1

12 2

Ex 3) Determine whether the following is true or false.

2

3 3

?

?

?

Two Truths & a Lie

Two of the following statements are true and one is a lie.Find the “lie” and fix it to make it a truth.

A) B) C) 5 7sec( ) 1 csc 2 cot 3

6 6

7cot 3

6

Use whiteboards

Homework

#719 Pg. 438 1 – 43 odd