Name that Quadrant…

If cosθ>0 and sinθ<0, then θ is in what quadrant?

Cosθ is positive in which quadrants?

1 and 4

Sinθ is negative in which quadrants?

3 and 4

Quadrant 4

Name that Quadrant…

If cosθ<0 and sinθ<0, then θ is in what quadrant?

Cosθ is negative in which quadrants?

2 and 3

Sinθ is negative in which quadrants?

3 and 4

Quadrant 3

Name that Quadrant…

If cosθ>0 and sinθ>0, then θ is in what quadrant?

Cosθ is positive in which quadrants?

1 and 4

Sinθ is positive in which quadrants?

1 and 2

Quadrant 1

Name that Quadrant…

If tanθ>0 and sinθ<0, then θ is in what quadrant?

Tanθ is positive in which quadrants?

1 and 3

Sinθ is negative in which quadrants?

3 and 4

Quadrant 3

Name that Quadrant…

If cosθ>0 and tanθ<0, then θ is in what quadrant?

Cosθ is positive in which quadrants?

1 and 4

Tanθ is negative in which quadrants?

2 and 4

Quadrant 4

If the terminal side of angle θ goes through the point (, ) on the unit circle, find:

sinθ

cosθ

tanθ

¿ √𝟐𝟐

(𝒊𝒏𝒕𝒉𝒆𝒖𝒏𝒊𝒕𝒄𝒊𝒓𝒄𝒍𝒆 ,𝒚 𝒄𝒐𝒐𝒓𝒅𝒊𝒏𝒂𝒕𝒆=𝒔𝒊𝒏θ)

¿ √𝟐𝟐

(𝒊𝒏𝒕𝒉𝒆𝒖𝒏𝒊𝒕𝒄𝒊𝒓𝒄𝒍𝒆 ,𝒙 𝒄𝒐𝒐𝒓𝒅𝒊𝒏𝒂𝒕𝒆=𝒄𝒐𝒔 θ)

¿𝟏(𝒊𝒏𝒕𝒉𝒆𝒖𝒏𝒊𝒕 𝒄𝒊𝒓𝒄𝒍𝒆 ,𝒕𝒂𝒏θ=𝒙=𝒔𝒊𝒏θ𝒄𝒐𝒔 θ

)

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(𝒊𝒏𝒕𝒉𝒆𝒖𝒏𝒊𝒕 𝒄𝒊𝒓𝒄𝒍𝒆 , 𝒚 𝒄𝒐𝒐𝒓𝒅𝒊𝒏𝒂𝒕𝒆=𝒔𝒊𝒏θ)

¿−𝟎 .𝟔(𝒊𝒏𝒕𝒉𝒆𝒖𝒏𝒊𝒕 𝒄𝒊𝒓𝒄𝒍𝒆 ,𝒙 𝒄𝒐𝒐𝒓𝒅𝒊𝒏𝒂𝒕𝒆=𝒄𝒐𝒔 θ)

¿𝟎 .𝟖−𝟎 .𝟔

=𝟒−𝟑

(𝒊𝒏𝒕𝒉𝒆𝒖𝒏𝒊𝒕𝒄𝒊𝒓𝒄𝒍𝒆 ,𝒕𝒂𝒏θ=𝒙=𝒔𝒊𝒏θ𝒄𝒐𝒔 θ

)

If the terminal side of angle θ goes through the point (-, -) on the unit circle, find:

sinθ

cosθ

tanθ

¿−𝟓𝟏𝟑

(𝒊𝒏𝒕𝒉𝒆𝒖𝒏𝒊𝒕 𝒄𝒊𝒓𝒄𝒍𝒆 , 𝒚 𝒄𝒐𝒐𝒓𝒅𝒊𝒏𝒂𝒕𝒆=𝒔𝒊𝒏θ)

¿−𝟏𝟐𝟏𝟑

(𝒊𝒏𝒕𝒉𝒆𝒖𝒏𝒊𝒕 𝒄𝒊𝒓𝒄𝒍𝒆 , 𝒙𝒄𝒐𝒐𝒓𝒅𝒊𝒏𝒂𝒕𝒆=𝒄𝒐𝒔 θ)

¿𝟓𝟏𝟐

(𝒊𝒏𝒕𝒉𝒆𝒖𝒏𝒊𝒕𝒄𝒊𝒓𝒄𝒍𝒆 ,𝒕𝒂𝒏θ=𝒙=𝒔𝒊𝒏θ𝒄𝒐𝒔 θ

)

Factoring FebruaryFactor Completely:

Factor by Grouping

Greatest Common Factor Trinomial Factoring

Trigonometric CO-FunctionsThe 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!!!

Trigonometric CO-Functions

http://www.ck12.org/trigonometry/Cofunction-Identities-and-Reflection/lesson/user:Yy5jYW1wYmVsbEBod3NjaG9vbHMubmV0/Cofunction-Identities/

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

Practice with CO-functions

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°

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°

Exact Values with Reciprocal Functions

1) csc 150°

Find the exact value of each expression:

30°1

-

2 csc θ = (reciprocal of sine)

Draw the reference triangle and label the sides.

csc θ = = 2 (reciprocal of sine)

Exact Values with Reciprocal Functions

2) cot 360°

Find the exact value of each expression:

cot θ = (reciprocal of tangent)

cos θ = x , sin θ = y 360° is at (1,0)

This is a quadrantal angle.

cot 360° = = undefined

Exact Values with Reciprocal Functions

3) sec 225°

Find the exact value of each expression:

sec θ = (reciprocal of cos) =- = -

4) tan 45°· sec 30°5) cos 45° + sec 120°6) csc 90° + sec 180°

=

=

= 0

Name that Quadrant…

7) cot x<0 and sin x>0

2

9) csc θ<0 and tan θ>0

28) sec θ<0 and csc θ>0

3

If sinθ = = -, find the following:

a) cotθ b) secθ c) tanθ d) cscθ

¿−𝟒𝟑

¿−𝟓𝟒

¿−𝟑𝟒

¿𝟓𝟑

If cscθ =- = -, find the following:

a) cotθ b) secθ c) tanθ d) sinθ

¿ √𝟓𝟐

¿ 𝟐√𝟓𝟓

¿−𝟐𝟑

¿−𝟑√𝟓𝟓