Signs of Trigonometric Functions
The signs of the trigonometric functions for different values of θ can be determined
by noting the signs of x and y in the unit circle:
y
1
2nd quadrant
x negative
y positive
1st quadrant
x positive
y positive
y
1
x 1
x
3rd quadrant
x negative
y negative
y
x
4th quadrant
x positive
y negative
75
‘CAST’ Diagram
sin θ =
Since in the unit circle sin θ = y, cos θ = x and tan θ = cos
θ
following ‘CAST’ diagram as a shorthand for remembering signs
functions in different parts of the circle:
y
x , we obtain the
of trigonometric
y
1
ALL sin, cos, tan positive
only SIN positive
S
A
1
T
only TAN positive
x
C
only COS positive
76