Pre-college Math

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Transcript Pre-college Math 

PRE-COLLEGE MATH
Section 6
January 8, 2015
LABELING TRIANGLES
B
Opposite of A
Adjacent of B
Hypotenuse
A
Opposite of B
Adjacent of A
We label the other two angles (non90° ) angles as A and B. We then
label the sides accordingly. The side
that is opposite from angle A is the
adjacent to angle B and vice versa.
The side that is opposite from the 90°
is always the hypotenuse.
These labels are important for the
next phase of this lesson.
RATIOS IN TRIANGLES
The next step of this lesson is to talk about
ratios.
Ratios are fractions which relate two
quantities. When these quantities have similar
units of measure (for example length, weight,
etc) then the ratio has NO unit of measure.
TANGENT RATIO
β€’ The tangent ratio of an angle in a triangle is given by the opposite side of the
angle over the adjacent side.
β€’ It is written as follows:
π‘‚π‘π‘π‘œπ‘ π‘–π‘‘π‘’ π‘œπ‘“ 𝐴
tan(𝐴) =
π΄π‘‘π‘—π‘Žπ‘π‘’π‘›π‘‘ π‘œπ‘“ 𝐴
π‘‚π‘π‘π‘œπ‘ π‘–π‘‘π‘’ π‘œπ‘“ 𝐡
tan(𝐡) =
π΄π‘‘π‘—π‘Žπ‘π‘’π‘›π‘‘ π‘œπ‘“ 𝐡
SINE RATIO
β€’ The sine ratio of an angle in a triangle is given by the opposite side of the
angle over the hypotenuse of the triangle.
β€’ It is written as follows:
π‘‚π‘π‘π‘œπ‘ π‘–π‘‘π‘’ π‘œπ‘“ 𝐴
sin(𝐴) =
π»π‘¦π‘π‘œπ‘‘π‘’π‘›π‘’π‘ π‘’
π‘‚π‘π‘π‘œπ‘ π‘–π‘‘π‘’ π‘œπ‘“ 𝐡
sin(𝐡) =
π»π‘¦π‘π‘œπ‘‘π‘’π‘›π‘’π‘ π‘’
COSINE RATIO
β€’ The cosine ratio of an angle in a triangle is given by the adjacent side of the
angle over the hypotenuse of the triangle.
β€’ It is written as follows:
π΄π‘‘π‘—π‘Žπ‘π‘’π‘›π‘‘ π‘œπ‘“ 𝐴
cos(𝐴) =
π»π‘¦π‘π‘œπ‘‘π‘’π‘›π‘’π‘ π‘’
π΄π‘‘π‘—π‘Žπ‘π‘’π‘›π‘‘ π‘œπ‘“ 𝐡
cos(𝐡) =
π»π‘¦π‘π‘œπ‘‘π‘’π‘›π‘’π‘ π‘’
NOTICE ANYTHING???
β€’ Did you notice anything about the sine and cosine
ratios?
β€’ Remember how the opposite side of the angle A
was the same as the adjacent side of the angle B?
β€’ The sine of angle A and the cosine of angle B are
the same.
β€’ Similarly, the sine of angle B and the cosine of angle
A are the same.
EXAMPLE 1
sin 𝐴 =
sin 𝐡 =
cos 𝐴 =
cos 𝐡 =
tan 𝐴 =
tan 𝐡 =
EXAMPLE 1- SOLUTION
sin 𝐴 =
12
15
=
4
5
sin 𝐡 =
9
15
=
3
5
cos 𝐴 =
9
15
=
3
5
cos 𝐡 =
12
15
=
4
5
tan 𝐴 =
12
9
=
4
3
tan 𝐡 =
9
12
=
3
4
HARD TO REMEMBER??
β€’ Worried about remembering the different ratios?
β€’ Just remember:
SOH CAH TOA
S
O
H
C
A
H
T
O
A
SO WHAT ELSE CAN WE DO?
β€’ Your calculator can give you a value of the sine,
cosine and tangent of an angle.
β€’ First you need to verify that your calculator is set to
the correct mode: degrees
β€’ The next thing that you need to do is locate the sin,
cos, and tan keys on the calculator.
THIS IS FAIRLY SIMPLE
To complete these types of problems all you have to
do is put them into the calculator and write down the
answer.
Let’s try it 
EXAMPLE 2
β€’ Compute the following:
1. sin 84°
2. cos 91°
3. tan 23°
4. sin 54°
5. tan 19°
6. cos 103°
EXAMPLE 2- SOLUTIONS
β€’ Compute the following:
1. sin 84° = 0.9945
2. cos 91° = βˆ’.0175
3. tan 23° = 0.4245
4. sin 54° = 0.8090
5. tan 19° = 0.3443
6. cos 103° = βˆ’.2250
HOMEWORK
ASSIGNMENT 6-2
DUE JANUARY 12, 2015