Sin and Cosine

3 ­ Sine and Cosine may 4.notebook
May 06, 2015
right triangle trigonometry
Trigonometry comes from the Greek words trigonon and metria meaning "triangle measurement."
The OPPOSITE is the side opposite the angle you are working with.
The Greek mathematicians Hipparchus of Nicaea and Ptolemy created the discipline of trigonometry more than 2000 years ago, primarily to study astronomy.
From Last Class . . .
tan θ =
opposite
adjacent
θ
The ADJACENT is the side which intersects the hypotenuse to form the angle.
opposite
hyp
ote
adjacent
nus
e
opposite
hypotenuse
Write the sine and cosine ratios as fractions.
θ
36
Today!
sin θ = The HYPOTENUSE is the side opposite the right angle.
15
cos θ = θ
sinθ = opposite hypotenuse
sinθ = 36
39
push
sinθ= 12
13
39
adjacent
hypotenuse
cosθ = adjacent hypotenuse
cosθ = 15
39push
cosθ = 5 13
What is the decimal number of each fraction?
0.9231
0.3846
What is the tan decimal? 2.4
Two important things to remember
:
1. Never find the ratios of the right angle.
2. Only the tangent can be greater than one.
If you know the acute angle, you can use a calculator to find the ratios as a rounded decimal to the nearest ten­thousandth.
example:
48o
sin 48o = .7431
push
cos 48o = .6691
3 ­ Sine and Cosine may 4.notebook
Find the value of x to the nearest tenth.
May 06, 2015
Find the value of x to the nearest tenth.
x
25o
25o
8
8
adj
cosθ = hyp
x
opp
sinθ = hyp
x
cos 25 = 8
o
(8)cos 25o = x
8
sin 25o = x
x = 7.3
(x)sin 25o = 8
x= 8
sin 25o
x = 18.9
Find θ rounded to the nearest degree.
19
7
θ
sinθ=7 19
θ = sin­1(7/19)
θ = 21.6
θ = 22
Quiz Next class
Homework pg. 372
#1-4ace, 6-7ace,8,9,10-11ace
Memorize!!!
sinθ = opp
hyp
cosθ = adj
hyp
tanθ = opp
adj