Download Example 1

March 28, 2016
8.1/6.1/6.2 Angles and
Their Measures (Day 1)
Objectives:
1. Use trig to find 6 trig fcns. (8.1)
2. Convert from degrees to radians and from
radians to degrees.(6.1)
3. Use a calculator to find the approx value of
the trig fcn. (6.2)
March 28, 2016
Right Triangle Trigonometry
(SOH CAH TOA...and beyond!)
B
Hyp
C
A
Sin θ =
Opp
Hyp
Csc θ =
Hyp
Opp
Cos θ =
Adj
Hyp
Sec θ =
Hyp
Adj
Cot θ =
Adj
Opp
Opp
Tan θ =
Adj
Notice the reciprocals: sine/cosecant
cosine/secant
tangent/cotangent
This means that
and so on...
March 28, 2016
Example 1: Find the exact value of the six trigonometric
functions of the angle θ in the figure.
5
θ
3
sin θ =
csc θ =
cos θ =
sec θ =
tan θ =
cot θ =
The 6 trig functions only depend on the size of the angle
NOT on the length of the sides.
March 28, 2016
Example 2: Find the exact value of the six trigonometric
functions of the angle θ in the figure.
5
θ
1
sin θ =
csc θ =
cos θ =
sec θ =
tan θ =
cot θ =
The 6 trig functions only depend on the size of the angle
NOT on the length of the sides.
March 28, 2016
Radians
Consider a circle of radius r. The
value of a radian is the measure
of a central angle on the circle
where the arc length on the circle
is equal to r. The measure of
such an angle is 1 radian.
r
r
r
radian
360o = 2π radians
Converting
Radians/degrees are an alternate ways to measure angles,
similar to feet/meters are alternate ways to measure length.
March 28, 2016
Example 3: Convert from degrees to radians or from
radians to degrees
1 degree =
60o
150o
-45o
90o
radians
1 radian =
degrees
March 28, 2016
Using a Calculator to Find
Trigonometric Functions.
Sine, Cosine and Tangent are on the face of the calculator.
To find Secant, Cosecant and Cotangent you must know the
reciprocal relationships.
The mode must also be in the correct unit....
degree or radian.
March 28, 2016
Example 4: Use the graphing calculator to find the
approximate values.
March 28, 2016
Homework:
Web Assignment 6.1 (& more!)
SOHCAHTOA