Download Welcome to Alg 2 / Trig!

Angles and Degree Measure
We will begin by measuring angles in degrees.
Recall that one degree is equal to 1/360 of a
complete revolution.
You can generate any angle by using a rotation
that moves one of the rays forming the angle,
called the initial side, onto the other ray, called
the terminal side.
Angles and Degree Measure
An angle is in standard position when its initial side coincides with
the positive x-axis. Angles can be classified by where their
terminal side lands.
An angle is considered a quadrantal angle when its terminal side
lies on a coordinate axis.
Angles and Degree Measure
Sketch each angle on your “whiteboard”. Then estimate the
measure of each of the following angles:
Angles and Degree Measure
Sketch the angle with the given measure on the coordinate axes.
170
Angles and Degree Measure
Sketch the angle with the given measure on the coordinate axes.
170
Angles and Degree Measure
Sketch the angle with the given measure on the coordinate axes.
190
Angles and Degree Measure
Sketch the angle with the given measure on the coordinate axes.
 210
Angles and Degree Measure
Sketch the angle with the given measure on the coordinate axes.
 300
Angles and Degree Measure
Sketch the angle with the given measure on the coordinate axes.
100
Angles and Degree Measure
Sketch the angle with the given measure on the coordinate axes.
 95
Angles and Degree Measure
Sketch the angle with the given measure on the coordinate axes.
450
Angles and Degree Measure
Sketch the angle with the given measure on the coordinate axes.
 400
Angles and Degree Measure
Sketch the angle with the given measure on the coordinate axes.
265
Angles and Degree Measure
Sketch the angle with the given measure on the coordinate axes.
 530
Angles and Degree Measure
Two angles in standard position are coterminal if their terminal
sides coincide.
Ex) Find two coterminal angles for the angle shown.
Angles and Degree Measure
To measure angles more precisely, consider how they can be
broken down:
Angles and Degree Measure
Ex) Convert 14 36' 54" to decimal degrees.
Ex) Convert 72.568 to degrees, minutes, and seconds
Learning Log Summary
LT 1 – I can use degree measure to sketch an
angle in standard position and convert
between different forms of degree measure.
Angles in standard position…
Positive vs negative angles are…
Coterminal angles are…
Trigonometric Functions
To define the trigonometric functions of an angle θ, place θ in
standard position. Then choose any point P (x,y) on the terminal
side of θ and let r be the distance OP.
Trigonometric Functions
An acute angle θ is in standard position and its terminal side
passes through (6 , 8). Find sinθ, cosθ and tanθ.
Trigonometric Functions
An acute angle θ is in standard position and its terminal side
passes through (3 , 5). Find sinθ, cosθ and tanθ.
Trigonometric Functions
Find sinθ and tanθ if θ is an acute angle and if cosθ=2/7.
Trigonometric Functions
Find sinθ and cosθ if θ is an acute angle and if tanθ=8/3.
Trigonometric Functions
If cosθ=3/4, find the value of cos(- θ).
Trigonometric Functions
If sinθ=1/2, find the value of sin(180- θ).
Trigonometric Functions
Trigonometric Functions
Trigonometric Functions
Learning Log Summary
LT 2 – I can define the sin, cos, and tan of an
angle using a point on the terminal side of the
angle.
Sin, Cos, Tan of an angle are…
To find the missing side of a right triangle…
If given the value of a trig function of an angle…
Closure
Homework
Problem Set #1
(Copy of Book Pages)
Warm-Up
Find the measure of the missing side/angle in each diagram.
Round answers to the nearest hundredth.
Law of Cosines
Law of Cosines
In a general triangle ABC:
a  b  c  2bc cos A
2
2
2
b  a  c  2ac cos B
2
2
2
c  a  b  2ab cos C
2
2
2
To use the Law of Cosines…
Law of Cosines
Ex 1) Find the length of side a to the nearest hundredth:
Law of Cosines
Ex 2) Find the length of side c to the nearest hundredth:
Law of Cosines
Ex 3) Find the measure of each angle of triangle ABC in the
diagram below.
Law of Cosines
Ex 4) A navigator plots the course a plane is currently traveling. The
plane is 300 miles from its destination. If it continues on its current
course it will travel 325 miles and end up 125 miles due south of its
destination. To the nearest degree, how many degrees is the plane
off course?
Learning Log Summary
LT 8 – I can apply the law of cosines to find
missing sides and angles of any triangle.
The Law of Cosines is useful if…
To find a missing side/angle using the Law of
Cosines…
Closure
Homework
pg. 582 ~ 1-11 (Odd)
pg. 583 ~ 1-7 (odd)
Law of Cosines – Partner Problems!
Law of Cosines – Partner Problems!
Law of Cosines – Partner Problems!
Law of Cosines – Partner Problems!
Law of Cosines – Partner Problems!
Law of Cosines – Partner Problems!