Essential Question:
What are the six trig functions and how do you use them?
Remember from yesterday …
 sin (θ) =
 cos (θ) =
 tan (θ) =
To define the other three functions, we find the reciprocal of sine,
cosine, and tangent.
Vocabulary:
 cosecant:
 secant:
 cotangent:
Short Hand:
 csc (θ) =
 sec(θ) =
 cot (θ) =
Example 1: Find the cotangent, secant, and cosecant of the angle shown.
Approximate to two decimal places.

a)
b)
5
3
5

3
4
4
c)

5
d) find all six ratios
2
7
1
7

5
Example 2: If
𝑠𝑖𝑛 𝜃 =
12
, find the other five trig functions.
13

Steps:
1-
We know by definition that sine is opposite over hypotenuse so
the opposite side will be _____ and the hypotenuse will be ____.
Label this on the triangle.
2 – To find the length of the missing side, we use the
3 – Now we have all three parts of the triangle, so we can define all
six functions.
sin (θ) =
tan (θ) =
sec (θ) =
cos(θ) =
csc (θ) =
cot (θ) =
8
a)
If cos (θ) =
b)
If cot (θ) =
c)
If sec (θ) = 3, find the other five function values.
17
4
3
find the other five function values.
find the other five function values.