1. U8D9
pencil, highlighter, red pen, calculator, notebook
Have out:
Bellwork:
1. 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. b. c.
2. Draw a sketch of . Then find THREE angles that are coterminal with .
total:

2. Bellwork: 1. 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.)
Bellwork: a.
The reference Δ is an isosceles right Δ.
Therefore, It is a Δ.
(45˚–45˚–90˚ Δ) y x +1 θ +2 +1 α 1 +1 +2
total:

3. 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.)
The reference Δ is a 30˚–60˚–90˚ Δ. b)
In radians, it is a Δ. y x
½ is the smallest side, so it must be opposite from the smallest angle, 30˚. θ
must be across from α = 60˚. α +2 1 +1 +1 +1 +2

4. 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) (1, 0) y x +1 +2 1
total:

5. 2. Draw a sketch of θ. Then find THREE angles that are coterminal with θ.
–72˚ + 360 +1
288o +1 θ x x θ +1 +1
–72˚ – 360 +1
–432o +1 +1 +1
648o or
–792o
or ? or
or ?
total:

6. Introduction to Trig Equations
Recall from previous lessons which trig functions are positive in each quadrant:
Remember:
All Students Take Calculus y x II
III IV I y x
sin
all
tan
cos
When we say 0 ≤ θ < 2π, we are considering ONE full rotation of the circle.

7. Introduction to Trig Equations
Example #1: Solve cos θ = for 0 ≤ θ < 2π.
cos θ > 0 in quadrants ___ and ___. I IV QI
Draw a sketch of θ for the ____ solution. y x
Label the sides of the reference triangle.
30–60–90
Hint: It’s a ____________ triangle. 
θ = 30°

8. This is the SAME reference triangle as in Q1, just rotated. Therefore:
Example #1: Solve cos θ = for 0 ≤ θ < 2π.
QIV
Draw a sketch of θ and α for the ____ solution. y x
Label the sides of the reference triangle.
This is the SAME reference triangle as in Q1, just rotated. Therefore:  α
Therefore, if we only know cos θ = for 0 ≤ θ < 2π, then there are 2 solutions:
and

9. Example #2: Solve cos θ = for 0 ≤ θ < 2π.
cos θ < 0 in quadrants ___ and ___. II
III y x
QII y x   α α
QIII

10. Work on the Practice. Example #3: Solve sin θ = 0 for 0 ≤ θ < 2π.
Since sin θ = ___ and r > ___, then sin θ = 0 means y = ___.
Where on a coordinate plane is y = ___?
x–axis y x
Work on the Practice.

11. cos θ < 0 in quadrants II and III.
Practice: Solve each equation for 0 ≤ θ < 2π. Draw sketches for each solution.
cos θ < 0 in quadrants II and III. a) y x
QII y x   α α
QIII

12. sin θ < 0 in quadrants III and IV.
Practice: Solve each equation for 0 ≤ θ < 2π. Draw sketches for each solution.
sin θ < 0 in quadrants III and IV. b) y x y x   α α
QIII
QIV

13. tan θ < 0 in quadrants II and IV.
Practice: Solve each equation for 0 ≤ θ < 2π. Draw sketches for each solution. c)
tan θ < 0 in quadrants II and IV.
QII y x y x   α α
QIV

14. Quiz Time After the quiz, work on the rest of the worksheet.
Clear your desk except for a pencil, highlighter, and a calculator!
After the quiz, work on the rest of the worksheet.

15. Finish the practice worksheets