14.2 Unit Circle Notes Date: Recall: Reciprocals of sine, cosine, and tangent

Reciprocal of sine:

Reciprocal of cosine: Reciprocal of tangent:

Unit circle: circle with radius 1 unit For every point on the unit circle, we can draw a right triangle: Using Right Triangle Trig, write down the following in terms of x and y:

sinT ____ cscT _____ cosT ____ secT _____ tanT ____ cotT _____ Therefore (x,y) =

Terminal Side on an Axis Assume this is a unit circle. Find sin, cos, tan.

Deg: Rad:

sin𝜃:

cos 𝜃:

tan 𝜃:

How to remember SIGNS of ALL trig ratios: ALL STUDENTS TAKE CALCULUS

You can use reference angles and special right triangles for trig ratios of angles that are not in Quadrant I.

Special Right Triangles:

Deg: Rad:

sin𝜃:

cos 𝜃:

tan 𝜃:

Find exact trig value using reference angle

sin−25𝜋6

Positive:

sin, csc

Positive:

tan, cot

Positive:

All

Positive:

cos, sec

dnskey 2016-2017

cosecant secant cotangentflip OPI flip Adi

fliptan0PPnypcgcO.hPhypsecOihMadjcotO.adIoppadjopp-Coohyp-1onaXes@qsingH0tanO-sindFradQNaooCOSOfxiuis9sinofTradWdM.IyytHM0ooradXxcopy360NTradslope.r

'T'd¥ g- ¥Trad 270°00 900 180 27003600(COSO

,sing 0 Fa it 3¥ 21T

• → -

ostelbyouwhat

's positive. O 1 0 -

/ O

S A Eu#

*%M* " ± 10to 1

Pwat¥fm?ftp.t#y,

F=t=¥=o÷o,

tinted

# T C IV

Ovndf. 0 undf

Othese

functions

w2

*¥o 3045060 /,¥n ref=#

1730

¥ 44 93 s Au .

B at

Boz

sina.DK#2 2+360,45kFF's

ftp.osicos#iz@@wd

't

7 45 FI 1 FsI

Bbenchmarksforvnitcirae !

©m 32L0u1n1g ZKuuitpaP HSaoUfstgwMaPrWeE BLbL1CU.9 I bAelAle NrFiyghhOtsss arcelsdeqrvvYemdY.3 Q PMjaSdqen 0wTivtvhQ MI1n7fcipnTihtNeX 4Ajl8gieCb7rxay 921.I Worksheet by Kuta Software LLC

Kuta Software - Infinite Algebra 2 Name___________________________________

Period____Date________________Exact Trig Values of Special Angles

Find the exact value of each trigonometric function.

1) tan

θ

x

y

60°

3

2) sin

θ

x

y

225°

−

2

2

3) sin

θ

x

y

90°

1

4) cos

θ

x

y

150°

−

3

2

5) cos

θ

x

y

90°

0

6) tan

θ

x

y

240°

3

7) cos

θ

x

y

135°

−

2

28) tan

θ

x

y

150°

−

3

3

-1-

Unitcirdews 'sANSKEYWHNH

is

: :Hoak

©I I2c0g1N1L zK2uZt9aO IS6o7fItawYatr0ee 1LYL8Cz.v I vAZlplu Vr1iVgehUtDsR HrxeIsuejrRvdeedu.1 N 7MxaQdre3 bw1iYtxhF TIMncfHi5nQi1tUe6 bAZlegwe3b4rzaY r2n.w Worksheet by Kuta Software LLC

9) cos

θ

x

y

270°

0

10) tan

θ

x

y

225°

1

11) cos 270°

0

12) sin 0

0

13) cot

7

π

4

−1

14) csc

2

π

3

2 3

3

15) csc 225°

− 2

16) sin 300°

−

3

2

17) csc 90°

1

18) tan 240°

3

19) sin

π

4

2

2

20) tan 120°

− 3

21) tan

−13

π

6

−

3

3

22) cos −630° 0

23) cos 990° 024) csc

−31

π

62

25) csc

−5

π

6−2 26) cos

−17

π

3

1

2

27) sin

29

π

6

1

2

28) sec 945°

− 2

29) cos

−11

π

2

0

30) sin −2

π

0

-2-

Create your own worksheets like this one with Infinite Algebra 2. Free trial available at KutaSoftware.com

f-convert !

# " "

is Ho#dn

EHan

AnsklfI

ao

SH' ' A

0 30 45 60 90 120 60135 Tyz 45

0 % My 73 172 150 #u 30

0 £ § It 1 in%

3604,0) (1/0)

1 It 53 £ 0 yo 330

0 B- 1 B

undefttfuo300×5 T C3

270 (051 )=B = B- =T3

2 a

600

= -2 =/ = - 2

0 = undef a

It = -2T =I33 3

=r± = . B ne3 2 2

= 's = 's = I

1 }s°reE45° }oooref=60° zw°ref=30°= - Fy =

- FE = -2

= 0 ==Ctdzjret "60 ,zz5y5 ,

}zo°retH= -2ps =-D = tr

3

yqsttirutso Moret " " gpooref:30°= - / =+£ =

- £

Unit Circle Worksheet C Name___________________ Period___________ The given point P is located on the Unit Circle. State the quadrant and find the angle , also sin , cos and tan .

1) 1 3,2 2

P 2) (0, 1)P 3) 2 2,2 2

P

Quad: Quad: Quad: sin : sin : sin :

cos : cos : cos : tan : tan : tan : Find the exact value of each function.

4) 7cos4

5) sin 30D 6) 2sin3

7) cos(600 )D 8) 9sin2

9) tan(7 )

10) 11cos4

11) sin 225D 12) tan(585 )D

13) cos(1440 )D 14) 13sin4

15) 23cos6

Anstey

in radiansanddegas• , ,µ 0=2700 0=225 k¥

=2+T= 372=5H#3

onyaxis #4

+5-3- 1

- Brs o - r¥- 8 undef

.+1is#3±fF=now#

&¥¥tta⇒'s:P¥ir£= . 's =1 =O

=t£ =rz⇒.

§=T3¥5B#oa

2 a

use

:q#YEo