Download 10.4-10.5 Sine, Cosine, Tangent

Section 10.4 and 10.5: Sine-Cosine-Tangent
Opposite/Adjacent/Hypotenuse
To understand sine, cosine, and tangent, you must be able to find label sides as adjacent or opposite of an angle.
What side is the hypotenuse?
B
c
a
C
What side is opposite of
A?
What side is adjacent to
A?
What side is opposite of
B?
What side is adjacent to
B?
A
b
Sine (sin)
The sine (or shorthand sin) is simply a ratio in a right triangle comparing the side opposite an angle to the
hypotenuse.
For example, sin 40
64
100
16
25
Sine (sin) / Cosine(cos) / Tangent(tan)
To remember the trigonometric ratio we can use the following saying:
Sin = _________
Cos = _________
Tan = _________
Using the triangle below express sine-cosine-tangent.
B
5
3
C
4
sin A = --------
sin B = -------
cos A = -------
cos B = -------
tan A = -------
tan B = -------
A
Examples: Use the triangle below to find sin, cos, tan. NO DECIMALS!
1. sin A =
2. cos A =
3. tan A =
4. sin B =
B
C
7
25
A
5. cos B =
6. tan B =
Finding Missing Sides
You can find trigonometric ratios using your calculator!
**** Make sure your calculator is in _________________****
Examples: Find the values using your calculator
7. sin 45o
8. cos 87o
9. tan 37o
Examples: Find the missing side lengths.
10.
11.
B
X
12.
13.
A
34
10
Y
C
15. A 15-foot ladder leans against a wall. The angle of elevation (the angle between the ladder and ground)
is 70o. How far up the wall does the ladder reach?