Warm-Up 1-13
Three gears in a machine
are positioned relative to
each other to form an
isosceles right triangle as
shown below. What is the
distance between the
center of the gears
located at B and C?
Leave your answer in
simplest radical form.
Announcements
 Test
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Next Thursday
Special Right Triangles
Trig
 Online
Homework 10-3 Due Sunday Night
Trigonometry
Parts of a right triangle
When is it used?
 Before
the 16th century trig was used to
determine position of stars and planets
 Here are some of the fields that use
trigonometry TODAY
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Astronomy
Navigation
Game Development
Engineering
Number Theory
Architecture
Pharmacy
Biology
Physics
Music Theory
And the list goes on…
Definitions
 Reference
Angle (θ) – the angle we
are using
 Hypotenuse- in a right triangle, it is
the longest side of the triangle and
it is located across from the right
angle
 Adjacent- The side that is adjacent,
beside, next to, or touching θ
 Opposite- The side opposite of θ
Label the sides of the triangles,
given the reference angle.
Look at the frist two triangles... How are
they the same? How are they different?
As
the reference angle
changes, the adjacent and
opposite sides change, but
the hypotenuse always stays
the same
Three Trig Ratios
Sine
Abbreviated
as sin
Cosine
Abbreviated
as cos
Tangent
Abbreviated
as tan
Trig Ratios(Sine, Cosine,
Tangent)
 sin(θ)
 cos
 tan
=
𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒
𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
(θ) =
θ=
𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡
𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
𝑂𝑝𝑝𝑜𝑠𝑖𝑡𝑒
𝐴𝑑𝑗𝑎𝑐𝑒𝑛𝑡
SOH
CAH
TOA
S O H C A H
T
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p
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p
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Setting up trig ratios
1.
2.
3.
4.
5.
Mark the angle you are using
Label the sides in relation to the
reference angle (opp, adj, hyp)
Circle the two sides that you will be
used in the trig ratio (use
SOHCAHTOA)
Decide which side goes on top
and which side goes on bottom
Write the fraction (and simplify!)
Practice
Practice
Practice
Homework
Online
Homework due
Sunday night
Classwork
Pg.
438 #1-9 just write
the ratios, don’t solve
for x.