1. U8D8
pencil, highlighter, red pen, calculator, notebook
Have out:
Bellwork:
Given the point (1, ) on the terminal side of θ,
Plot the point
Show θ and α
Draw the reference triangle
Label x, y, and r.
Find sinθ, cosθ, and tanθ.
Find θ in radians +1 y +2 +1 +1 θ x α
total:

2. Given the point (1, ) on the terminal side of θ,
v) Find sinθ, cosθ, and tanθ.
vi) Find θ in radians +2
Note the ratio of the sides. It’s a special right triangle +2 y +2
Recall: 60 = θ x +1 α
60
30 +2
total:

3.  Given r = 1, find the coordinates of x and y for the angles θ with a reference angle of .
= 0˚ y
= 0
( , ) 1 1 x

4. is the same as what degree?
 Given r = 1, find the coordinates of x and y for the angles θ with a reference angle of b)
= 90˚
is the same as what degree? y
( , ) 1 1 θ
= undefined x

5.  Given r = 1, find the coordinates of x and y for the angles θ with a reference angle of .
= 180˚ y θ
= 0 1 x
( , ) –1

6.  Given r = 1, find the coordinates of x and y for the angles θ with a reference angle of .
= 270˚ y θ
= undefined x 1
( , ) –1

7. Recall from yesterday:
Given reference angle , and
Given reference angle , and
Given reference angle , and
Notice that the denominators are always equal to 2.
Notice that and have the cosine and sine values switched.
Let’s put it all together using some patterns:

8. θ Fill in the values for common angles. sinθ cosθ tanθ = 0 = 1 = 1 = 0
sinθ
cosθ
tanθ
= 0
= 1
= 1
= 0
= 0 1
= undefined
Use the identity to find tanθ.

9. The reference Δ is an isosceles right Δ.
Practice: If the given point is on the terminal side of , (i) plot the point on a unit circle, (ii) show , (iii) determine the radian measure of . (Try not to look at your notes.) a)
The reference Δ is an isosceles right Δ.
Therefore, It is a Δ.
(45˚–45˚–90˚ Δ) y x 1 θ

10. Practice: If the given point is on the terminal side of , (i) plot the point on a unit circle, (ii) show , (iii) determine the radian measure of . (Try not to look at your notes.)
b) (0, 1) y x 1 θ

11. The reference Δ is a 30˚–60˚–90˚ Δ.
Practice: If the given point is on the terminal side of , (i) plot the point on a unit circle, (ii) show , (iii) determine the radian measure of . (Try not to look at your notes.) c)
The reference Δ is a 30˚–60˚–90˚ Δ.
In radians, it is a Δ. y x
½ is the smallest side, so it must be opposite from the smallest angle, 30˚. 1 θ

12. The reference Δ is a 30˚–60˚–90˚ Δ. d)
Practice: If the given point is on the terminal side of , (i) plot the point on a unit circle, (ii) show , (iii) determine the radian measure of . (Try not to look at your notes.)
The reference Δ is a 30˚–60˚–90˚ Δ. d)
In radians, it is a Δ. y x
½ is the smallest side, so it must be opposite from the smallest angle, 30˚. 1 θ
must be across from α = 60˚. α

13. It’s time for the…
Quiz
Clear your desks except for a pencil and highlighter.
When finished, flip your quiz over, we are going to grade the quiz in class in a few minutes.
Your assignment: Finish the worksheets.

14. Take out a red pen, it’s time to grade the quiz.

15. 90˚ 120˚ 60˚ 135˚ 45˚ 150˚ 30˚ 0˚ Each answer is 1 point. 180˚ 360˚y
60˚
135˚
45˚
150˚
30˚ 0˚
Each answer is 1 point. x
180˚
360˚
210˚
330˚
225˚
315˚
240˚
300˚
270˚

16. Finish the practice worksheets