Download Right Triangle Trigonometry

Section 4-1
What we know. Click on any that apply to be true
about right triangles.
0%A. Right triangles have a 180 degrees in them
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B. Right triangles have a 90 degree angle
C. Trigonometry can be used on any type of triangle.
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D. There are 4 main trigonometric functions.
0%E. There is only one way to always look at any of these
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problems.
Vocabulary
 Trigonometry: The study of relationships among
the angles and sides of a right triangle.
 Trigonometric ratio: compares the sides lengths of a
right triangle.
 Trigonometric Functions: has a rules given by a
trigonometric ratio
A. Sine
B. Main
C. Cosine
Choose the six basic
trigonometric Functions.
Choose any that apply.
D. Tangent
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E. Peroant
F. Cosecant
G. Secant
H. Cotangent
I. Gauss
J. Cosme
Sine
Main
Cosine
Tangent
Peroant
Gauss
Cosecant
Cosme
Secant
Cotangent
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Countdown
Trig Functions of Right Triangles
 Sine (sin)θ =
𝑜𝑝𝑝
ℎ𝑦𝑝
 Cosine (cos)θ =
 Cosecant (csc)θ =
𝑎𝑑𝑗
ℎ𝑦𝑝
 Tangent (tan)θ =
𝑜𝑝𝑝
𝑎𝑑𝑗
 Secant (sec)θ =
ℎ𝑦𝑝
𝑜𝑝𝑝
ℎ𝑦𝑝
𝑎𝑑𝑗
 Cotangent (cot)θ =
𝑎𝑑𝑗
𝑜𝑝𝑝
Evaluate the six trigonometric
functions.
17
8
𝜃
15
Special Triangles
600
450
2x
x
𝑥 2
x
300
x 3
450
x
Find the missing side length
10
8
x
x
300
450
Inverse Trig Functions
 Allows us to know side lengths and find missing angles.
 Have all six trig functions still
 sin−1

1
sin−1
, cos −1
= csc −1
, tan−1
,
1
cos−1
= sec −1
, and
1
tan−1
= cot −1
Place the six trig functions with their correct association.
a = sin, b = cos, c = tan, d = csc, e = sec, f = cot.
𝑜𝑝𝑝
ℎ𝑦𝑝
ℎ𝑦𝑝
𝑜𝑝𝑝
𝑎𝑑𝑗
𝑎𝑑𝑗
1=
,2 =
,3 =
,4 =
, 5 = 𝑜𝑝𝑝 , 6 = ℎ𝑦𝑝 ,
ℎ𝑦𝑝
𝑎𝑑𝑗
𝑜𝑝𝑝
𝑎𝑑𝑗
A. a1,b6, c2, d3, e5, f4
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B. a1, b6, c4, d2, e4, f5
C. a1, b6, c5, d2, e3, f4,
D. a1, b6, c4, d3,e2, f5
E. a1, b6, c2, d5, e4, f3
a1,b6, c2, d3, e5...
a1, b6, c4, d2, e...
a1, b6, c4, d3,e...
a1, b6, c2, d5, e...
a1, b6, c5, d2, e...
180
Countdown
A hot air balloon that is
moving above a
neighborhood has an angle
of depression of 28 degrees
to on house and 52 degrees
to a house down the street.
If the height of the balloon
is 650 ft, estimate the
distance between the two
houses.
Determine your comfort level with the material so
far…
A. I got this!
B. I have about 75% of
0%
this!
C. I am getting there!
D. I am lost!
I got this!
I have about 75% ...
I am getting there!
I am lost!
10
Countdown
 Homework
 Section 4-1 pg 227 4, 28, 30,
39, 42, 43, 45, 57-68