Trigonometry Handout

Trigonometry
5) Signs
The signs of the trig functions for angles in each quadrant can be remembered by
the following saying:
All Students Take Calculus
Quad I: All ratios are positive
S
A
Quad II: Sine and cosecant are positive
Rest are negative
Quad III: Tangent and cotangent are positive
Rest are negative
T
C
Quad IV: Cosine and secant are positive
Rest are negative
Figure 10
3π
Example 3: Let P = (−1,1 ) be a point on the terminal side of the angle θ = . Find the
4
exact trigonometric ratios for θ .
Solution: Since P = (−1,1 ) is a point on the terminal side of the angle
2 2
( −1)
+ (1) = 2 ⇒ r = 2
1
-1
P
θ
sinθ
=
1
2
=
2
2
cscθ
=
2
1
=
2
cosθ
=
−1
2
=
−
2
2
secθ
=
2
−1
= −
2
tanθ
=
1
−1
= −1
−1
cotθ
= = −1
1
Page 7 of 23