Chapter 1 and 2 Summary Sheet
(x,y)
1st Definition of the six trig functions:
y
r
sin  
r
csc  
r
y
r
x
r  x2  y 2
sec  
cos  
x
r
y
x
r is the distance from the point (x,y) to the origin.
tan  
cot  
x
y
Trigonometric Identities:
Pythagorean:
𝟐
𝟐
𝐬𝐢𝐧 𝜽 + 𝐜𝐨𝐬 𝜽 = 𝟏
𝐭𝐚𝐧𝟐 𝜽 + 𝟏 = 𝐬𝐞𝐜 𝟐 𝜽
𝟏 + 𝐜𝐨𝐭 𝟐 𝜽 = 𝐜𝐬𝐜 𝟐 𝜽
Reciprocal
1
csc  
sin 
1
sec  
cos 
1
cot  
tan 
Quotient
Cofunction
sin 
cos 
cos 
cot  
sin 
tan  
cos(90° − 𝜃 ) = sin 𝜃 sin(90° − 𝜃 ) = cos 𝜃
sec(90° − 𝜃 ) = csc 𝜃 csc(90° − 𝜃 ) = sec 𝜃
tan(90° − 𝜃 ) = cot 𝜃 cot(90° − 𝜃 ) = tan 𝜃
2nd Definition of the 6 Trig Functions (acute angles – “right triangle definitions”)
sin  
opposite
hypotenuse
Special Triangles:
cos  
adjacent
hypotenuse
tan  
opposite
adjacent
Functions values of quadrantal and special angles:

0
90
180
270
360
Quadrantal Angles
sin 
0
1
0
-1
0
cos 
1
0
-1
0
1
tan 
0
undefined
0
undefined
0

0°
30°
45°
60°
90°
Special Angles (QI)
sin 
0
cos 
1
tan 
0
1/ 2
3/2
3/3
2/2
1/ 2
1
3
0
undefined
2/2
3/2
1
Signs of the 6 trig functions:
QII
sin  (+) csc (+)
cos  (-) sec (-)
tan  (-) cot (-)
sin  (+) csc (+)
cos  (+) sec (+) QI
tan  (+) cot (+)
QIII
sin  (-) csc (-)
cos  (-) sec (-)
tan  (+) cot (+)
sin  (-) csc (-)
cos  (+) sec (+) QIV
tan  (-) cot (-)
Range values for each trig function in interval notation:
sin  : [ 1,1]
csc  : (, 1]  [1, )
tan  : (, )
cos  : [ 1,1]
sec  : (, 1]  [1, )
cot  : (, )