Transcript trig File - Northwest ISD Moodle

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10.1-Intro to Trig
So what is Trigonometry?
It is one big, scary sounding word that really isn’t that scary!
Trigonon  Greek for “triangle”
Metron  Greek for “the measure of”
In fact, Trig (short for Trigonometry) makes our lives easier as
TRIANGLE EXPERTS!!!
That’s YOU!!!!
A
Let’s define some basic terms
for talking about the specific
parts of a ∆.
Trig ONLY works with
RIGHT ∆s!!
B
C
3 Angles: A, B, and C
3 Sides: AB, BC, and AC
The Basics
A
In Trig, the 3 sides are given special
names & you already know 1 of them!
The longest side of a RIGHT ∆
is the: HYPOTENUSE
B
Remember, the
Hypotenuse is always across
C
from the 90° angle!
The Basics
A
B
OPPOSITE
For the other 2 special sides,
we must use a particular
angle as a reference. Let’s
look at <A.
If you were standing at <A,
which side would be
across from you?
We call that the:
C
OPPOSITE SIDE
The Basics
A
ADJACENT
Still using <A as a reference…
If you were standing at <A,
which side would be
next to you?
B
We call that the:
ADJACENT SIDE
C
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End
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Draw each of the following
∆s & label the 3 sides based
on the < we are referencing
(as shown by the person):
Let’s Label
And the answers are…
Did you get them all correct?
OPPOSITE
ADJACENT
ADJACENT
OPPOSITE
ADJACENT
OPPOSITE
Now you try
What’s the Point?
You may be wondering how this could help us. If so, you aren’t
alone!
But let me ask you this…
How could we solve the following problem with only the info given
below?
Pythagorean Thm? NO
Right ∆ Ratios? NO
?
Trig? YES
40°
50 m
A trig ratio is a ratio of the lengths
of 2 sides of a right triangle
Opposite
Adjacent
Hypotenuse
The 3 basic trig ratios are:
sine (sin)
cosine (cos)
tangent (tan)
Here are their ratios:
𝒐𝒑𝒑𝒐𝒔𝒊𝒕𝒆
sin =
𝒉𝒚𝒑𝒐𝒕𝒆𝒏𝒖𝒔𝒆
cos =
𝒂𝒅𝒋𝒂𝒄𝒆𝒏𝒕
𝒉𝒚𝒑𝒐𝒕𝒆𝒏𝒖𝒔𝒆
tan =
𝒐𝒑𝒑𝒐𝒔𝒊𝒕𝒆
𝒂𝒅𝒋𝒂𝒄𝒆𝒏𝒕
Write as a
ratio
sin B
cos B
tan B
B
10
8
U
6
Write as a
ratio
sin S
cos S
tan S
S
Write as a
ratio:
sin z
tan x
tan z
cos x
cos z
sin x
Day 2
Be thankful you have a
calculator….because all of the trig
ratios are already programmed into
your calculator.
To use your calculator to find sides
of a right triangle you must change
your calculator into degree mode
Let’s practice finding the ratios
on the calculator.
Find:
tan 31
sin 20
cos 74
𝑻𝒉𝒆 𝑮𝒓𝒆𝒆𝒌 𝒔𝒚𝒎𝒃𝒐𝒍 𝜽 (theta)
represents a plane angle in
geometry
How can we use this to find the
sides of a right triangle?
71ᵒ
48
x
How can we use this to find the
sides of a right triangle?
What angle do I have?
What ratio is opposite
and adjacent?
ADJACENT
From the 71° angle, what
side do I have and what
side am I looking for?
tan 71° = x
48
71ᵒ
48
x = 48 tan 71
x
OPPOSITE
x = 139.4
OPPOSITE
OPPOSITE
ADJACENT
ADJACENT
What side am I looking
for?____________
What side do I
have?____________
What ratio should I
use?
_________________
sin 34° = x
12
12 sin 34°
x = 6.7
What side am I looking
for?____________
What side do I
have?____________
What ratio should I
use?
_________________
cos 24° = x
26
26 cos 24°
x = 23.75
OPPOSITE
ADJACENT
First label the sides from the given angle
ADJACENT
What side am I looking
for?____________
What side do I
have?____________
What ratio should I
use?
_________________
cos 50° = 20
x
cos 50 = 20
x
20
cos 50
x = 31.11
OPPOSITE
What side am I looking
for?____________
What side do I
have?____________
What ratio should I
use?
_________________
sin 53° = 22
b
sin 53 = 22
b
22
sin 53
b = 27.55
Find:
x = _______________
y = _______________
Find the measure of angle X.
From angle X:
What sides do I have?
I have the opposite and adjacent.
Which ratio should I use?
tan
Find the measure of angle C to the nearest tenth
From angle C:
What sides do I have?
opposite and hypotenuse
Which ratio should I use?
sin
Find the measure of angle C to the nearest tenth
From angle C:
What sides do I have?
adjacent and hypotenuse
Which ratio should I use?
Cosine
Find PN =
Find m<P
Find m<N