1. Quadrant 4 Name that Quadrant…
If cosθ>0 and sinθ<0, then θ is in what quadrant?
Quadrant 4
Cosθ is positive in which quadrants?
1 and 4
Sinθ is negative in which quadrants?
3 and 4

2. Quadrant 3 Name that Quadrant…
If cosθ<0 and sinθ<0, then θ is in what quadrant?
Cosθ is negative in which quadrants?
2 and 3
Quadrant 3
Sinθ is negative in which quadrants?
3 and 4

3. Quadrant 1 Name that Quadrant…
If cosθ>0 and sinθ>0, then θ is in what quadrant?
Cosθ is positive in which quadrants?
Quadrant 1
1 and 4
Sinθ is positive in which quadrants?
1 and 2

4. Quadrant 3 Name that Quadrant…
If tanθ>0 and sinθ<0, then θ is in what quadrant?
Tanθ is positive in which quadrants?
1 and 3
Quadrant 3
Sinθ is negative in which quadrants?
3 and 4

5. Quadrant 4 Name that Quadrant…
If cosθ>0 and tanθ<0, then θ is in what quadrant?
Quadrant 4
Cosθ is positive in which quadrants?
1 and 4
Tanθ is negative in which quadrants?
2 and 4

6. If the terminal side of angle θ goes through the point ( 𝟐 𝟐 , 𝟐 𝟐 ) on the unit circle, find:
sinθ
cosθ
tanθ
= 𝟐 𝟐 (𝒊𝒏 𝒕𝒉𝒆 𝒖𝒏𝒊𝒕 𝒄𝒊𝒓𝒄𝒍𝒆, 𝒚 𝒄𝒐𝒐𝒓𝒅𝒊𝒏𝒂𝒕𝒆=𝒔𝒊𝒏θ)
= 𝟐 𝟐 (𝒊𝒏 𝒕𝒉𝒆 𝒖𝒏𝒊𝒕 𝒄𝒊𝒓𝒄𝒍𝒆, 𝒙 𝒄𝒐𝒐𝒓𝒅𝒊𝒏𝒂𝒕𝒆=𝒄𝒐𝒔θ)
=𝟏 (𝒊𝒏 𝒕𝒉𝒆 𝒖𝒏𝒊𝒕 𝒄𝒊𝒓𝒄𝒍𝒆, 𝒕𝒂𝒏θ=𝒙= 𝒔𝒊𝒏θ 𝒄𝒐𝒔θ )

7. sinθ cosθ tanθ If the terminal side of angle θ goes through the point
(-0.6,0.8) on the unit circle, find:
sinθ
cosθ
tanθ
=𝟎.𝟖 (𝒊𝒏 𝒕𝒉𝒆 𝒖𝒏𝒊𝒕 𝒄𝒊𝒓𝒄𝒍𝒆, 𝒚 𝒄𝒐𝒐𝒓𝒅𝒊𝒏𝒂𝒕𝒆=𝒔𝒊𝒏θ)
=−𝟎.𝟔 (𝒊𝒏 𝒕𝒉𝒆 𝒖𝒏𝒊𝒕 𝒄𝒊𝒓𝒄𝒍𝒆, 𝒙 𝒄𝒐𝒐𝒓𝒅𝒊𝒏𝒂𝒕𝒆=𝒄𝒐𝒔θ)
= 𝟎.𝟖 −𝟎.𝟔 = 𝟒 −𝟑 (𝒊𝒏 𝒕𝒉𝒆 𝒖𝒏𝒊𝒕 𝒄𝒊𝒓𝒄𝒍𝒆, 𝒕𝒂𝒏θ=𝒙= 𝒔𝒊𝒏θ 𝒄𝒐𝒔θ )

8. sinθ cosθ tanθ If the terminal side of angle θ goes through the point
(- 𝟏𝟐 𝟏𝟑 , - 𝟓 𝟏𝟑 ) on the unit circle, find:
sinθ
cosθ
tanθ
=− 𝟓 𝟏𝟑 (𝒊𝒏 𝒕𝒉𝒆 𝒖𝒏𝒊𝒕 𝒄𝒊𝒓𝒄𝒍𝒆, 𝒚 𝒄𝒐𝒐𝒓𝒅𝒊𝒏𝒂𝒕𝒆=𝒔𝒊𝒏θ)
=− 𝟏𝟐 𝟏𝟑 (𝒊𝒏 𝒕𝒉𝒆 𝒖𝒏𝒊𝒕 𝒄𝒊𝒓𝒄𝒍𝒆, 𝒙 𝒄𝒐𝒐𝒓𝒅𝒊𝒏𝒂𝒕𝒆=𝒄𝒐𝒔θ)
= 𝟓 𝟏𝟐 (𝒊𝒏 𝒕𝒉𝒆 𝒖𝒏𝒊𝒕 𝒄𝒊𝒓𝒄𝒍𝒆, 𝒕𝒂𝒏θ=𝒙= 𝒔𝒊𝒏θ 𝒄𝒐𝒔θ )

9. Factoring February Factor Completely: 𝟏) 𝟔 𝒂 𝟐 +𝟗𝒂𝒃−𝟑𝒃−𝟐𝒂
𝟑𝒂 𝟐𝒂+𝟑𝒃 −𝟏(𝟐𝒂+𝟑𝒃) Factor by Grouping
(𝟐𝒂+𝟑𝒃)(𝟑𝒂−𝟏)
𝟐) 𝟗𝒂 𝟒 +𝟏𝟏 𝒂 𝟑 𝒃+ 𝟐𝒂 𝟐 𝒃 𝟐
𝒂 𝟐 (𝟗 𝒂 𝟐 +𝟏𝟏𝒂𝒃+𝟐 𝒃 𝟐 Greatest Common Factor
𝒂 𝟐 𝟗𝒂+𝟐𝒃 𝒂+𝒃 Trinomial Factoring

10. Trigonometric CO-Functions
The six trigonometric co-functions can be separated into 3 groups of two based on the prefix co:
sin and cosine
secant and cosecant
tangent and cotangent
Each of the groups are known as co-functions
The prefix co means complement or opposite
This is NOT to be confused with reciprocal functions!!!

11. Trigonometric CO-Functions
Watch the following video to learn about Co-functions. Stop the video at 4:56!!!!

12. Practice with CO-functions
Find the angle that makes each statement true.
c) csc 12° = sec β
a) cos 5° = sin β
d) sin 45° = cos β
e) tan β = cot (45°+2β)
f) sin (3β-15°) = cos (β +25°)
b) tan 60° = cot β
Since co-functions are complementary, set them = to 90°
β + 5° = 90°
β = 85°
β + 60° = 90°
β = 30°
β + 12° = 90°
β = 78°
β + 45 = 90°
β = 45°
β + 45° + 2β = 90°
3β= 45° β=15°
3β - 15° + β + 25° =90°
4β = 80° β = 20°

13. Exact Values with Reciprocal Functions
Find the exact value of each expression:
1) csc 150°
Draw the reference triangle and label the sides.
30° 1
- 3 2
csc θ = 𝒉𝒚𝒑𝒐𝒕𝒆𝒏𝒖𝒔 𝒐𝒑𝒑𝒐𝒔𝒊𝒕𝒆 (reciprocal of sine)
csc θ = 𝟐 𝟏 = 2 (reciprocal of sine)

14. Exact Values with Reciprocal Functions
Find the exact value of each expression:
2) cot 360°
This is a quadrantal angle.
cot θ = 𝒄𝒐𝒔θ 𝒔𝒊𝒏θ (reciprocal of tangent)
cos θ = x , sin θ = y 360° is at (1,0)
cot 360° = 𝟏 𝟎 = undefined

15. Exact Values with Reciprocal Functions
Find the exact value of each expression:
=- 𝟐 𝟏 = - 𝟐
3) sec 225°
sec θ = 𝒉𝒚𝒑𝒐𝒕𝒆𝒏𝒖𝒔𝒆 𝒂𝒅𝒋𝒂𝒄𝒆𝒏𝒕 (reciprocal of cos) =
4) tan 45°· sec 30°
= 2 −4 2
5) cos 45° + sec 120°
= 0
6) csc 90° + sec 180°

16. 2 2 3 Name that Quadrant… 7) cot x<0 and sin x>0
8) sec θ<0 and csc θ>0 3
9) csc θ<0 and tan θ>0

17. a) cotθ b) secθ c) tanθ d) cscθ
If sinθ = 𝟑 𝟓 𝐚𝐧𝐝 cosθ = - 𝟒 𝟓 , find the following:
a) cotθ b) secθ
c) tanθ d) cscθ
=− 𝟓 𝟒
=− 𝟒 𝟑
= 𝟓 𝟑
=− 𝟑 𝟒

18. a) cotθ b) secθ c) tanθ d) sinθ
If cscθ =- 𝟑 𝟐 𝐚𝐧𝐝 cosθ = - 𝟓 𝟑 , find the following:
a) cotθ b) secθ
c) tanθ d) sinθ
=− 𝟑 𝟓 𝟓
= 𝟓 𝟐
=− 𝟐 𝟑
= 𝟐 𝟓 𝟓