Download Example 1

March 29, 2016
6.1/6.2 Angles and Their
Measure (Day 2)
Objectives:
1. Draw an angle.
2. Find the reference angle.
3. Find the reference triangle.
4. Find the values of the 6 trig fcns given a
point on the terminal side of the triangle.
March 29, 2016
Don't write anything until we get to
Example 1, just pay attention!
Angles and Their Measure
Trigonometry Angles are different geometry angles...
The angles rotate around a point (like the origin) on a
coordinate graph.
They can rotate counter-clockwise (CCW) or clockwise
(CW). The measure is positive for a CCW rotation and
negative for a CW rotation.
The rotating ray of the angle is called the terminal side
and the starting point side is called the initial side.
Lower case Greek letters such as α (alpha), β (beta), γ
(gamma), θ (theta), and so on are used to name trig
angles.
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March 29, 2016
Standard Position - An angle is said to be in
standard position if its vertex is at the origin of a
rectangular coordinate system and its initial side
coincides with the positive x-axis.
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When an angle θ is in standard position, the terminal side
either will lie in a quadrant, in which case we say θ lies in
that quadrant, or it will lie on the x-axis or the y-axis, in
which case we say θ is a quadrantal angle.
II
I
III
IV
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Let's look at CCW rotations.
Negative
degrees
indicate CW
movement!
March 29, 2016
Angles are measured in degrees.
One rotation is
Example 1: Draw each angle.
1. 45o
3. 225o
2. -90o
4. 405o
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Knowing the reference angle will help us to find the trig
values for the angles.
The reference angle is the
positive acute angles formed
by the terminal side of the
angle nearest the x-axis.
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Example 2: Find the reference angle for each of the
following angles.
1. 94o
2. 245o
3. 290o
4. -110o
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Example 3: Find the Exact Values of the Six Trigonometric
Functions of an angle θ if (4, -3) is a point on its terminal side
sin θ =
cos θ =
tan θ =
csc θ =
sec θ =
cot θ =
draw a triangle
March 29, 2016
Example 4: Find the Exact Values of the Six Trigonometric
Functions of an angle θ if (-2, -3) is a point on its terminal side
sin θ =
cos θ =
tan θ =
csc θ =
sec θ =
cot θ =
draw a triangle
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y
-y
r
r
x
-x
r
r
y
-y
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S
A
T
C
All
Students
Take
Calculus
This memory trick lets you know the quadrants
where the trig ratios are positive (remember, if
sine is positive, so is cosecant, etc)
March 29, 2016
Example 5: Find the quadrant in which the angle lies.
March 29, 2016
Homework:
Web Assignment 6.1 (and then 6.2)
Trig Angles