Trigonometry Handout

Trigonometry
2) General Angles
Let θ be any angle in standard position
Let P ( x,
y)
be any point on the terminal side of θ
Let r be the distance from the origin to P (See Figure 9)
P ( x,
y)
Then,
sinθ
=
y
r
cscθ
=
r
y
r
θ
cosθ
=
x
r
secθ
=
r
x
O
Figure 9
tanθ
=
y
x
cotθ
=
x
y
Note: If y=0, then csc θ and cot θ are not defined. If x=0, then tan θ and sec θ are not
defined. These definitions are consistent with the previous definition if θ is an acute
angle.
3) Conventional Notation
If θ is a number, then by convention
of the angle whose radian measure is θ .
≈ where as sin( 5 ) ≈ 0. 0876
So, sin5
−9.
589
o
sin θ (or any trig function) means the sine
When using your calculator to compute trigonometric functions, you need to make sure
that your calculator is set to the correct mode. If you are computing radian measures, you
need to have your calculator in radians, and in degrees if you are computing degree
measures.
4) Some Common Angles:
Here is a table of common angles and the trig functions computed at them.
θ 0
sin θ 0
cos θ 1
tan θ 0
π
6
π
4
π
3
π
2
1
3
2 22
2
1
1
23
22
2
0
3 1 3 Und.
3
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