# Trig Functions Of Any Angle by 1FWEu5

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```									Trig Functions Of Any Angle
Evaluating

(x,y)

r

Definitions
• An angle  with terminal point (x,y) has
the following defined ratios:
sin = y/r cos = x/r tan = y/x csc = r/y
sec = r/x cot = x/y where r =√x2 + y2 or r2=x2+y2

EX: If (-3,4) is a terminal point, find trig values of 
r2 = (-3)2+42 so r=5
sin = 4/5 cos = -3/5 tan = -4/3
csc = 5/4 sec = -5/3 cot = -3/4

EX: If tan = - √3 find sin and sec. y = -√3 and x=1
r2 = 1 + 3 so r = 2 Then sin = -√3/2 and sec = 2

• Pos or neg values depend on the quad of 
S (-,+)      (+,+)A

T (-,-)      C (+,-)
 Trig values where terminal point of  is on
x or y axis. r = 1   (0,1)
(-1,0)       (1,0)

(0,-1)

cos = -1 sin =1 tan3 =undef cot0=undef
2       2
Reference Angles
•   If  is in standard position, its reference
angle  is the pos acute angle with x
axis


If  = 220 then =220-180 or 40
If  = 7 then  = 2- 7 or 
4                4    4
You try…
1.  = 100 2.  = 4 3.  =-2 4.  = 
3          3        6
Using Reference Angles

•     Trig function  = ± trig function 
EX: cos300 = cos60 = ½
sin300 = -sin60 = -√3 / 2
cot300 = -cot60 = -√3 / 3
Procedure: Find  find trig value decide ±
You try…
1. tan225 2. sec150 3. cos5 4. csc11
6
3

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