Trig Ratio Notes

Notes.notebook
March 05, 2014
© Ashley Spencer, 2014
Trigonometric Ratios
Find trigonometric ratios (Sine, Cosine, and Tangent) using right
triangles.
Common Core Standards:
G.SRT.6 Understand that by similarity, side ratios in right triangles
are properties of the angles in the triangle, leading to definitions of
trigonometric ratios for acute angles.
G.SRT.7 Explain and use the relationship between the sine and
cosine of complementary angles.
Jan 231:37 PM
Trigonometry Measure of Triangles
Trigonometric Ratio Ratio of two sides of a right triangle
Theta (Ɵ) Greek letter that is the reference angle in the triangle (used instead of a variable)
sine (sin)
e
opposite
us
ten
cosine (cos)
o
yp
h
tangent (tan)
Ɵ
adjacent
sin Ɵ = opposite
hypotenuse
cos Ɵ =
adjacent
hypotenuse
tan Ɵ =
opposite
adjacent
S =
Ways to remember:
O
H
A
C =
"SOHCAHTOA"
"Some Old Horse Caught Another Horse Taking Oats Away"
O
T =
Silently On Your Own: Can you think of your own phrase or shortcut?
H
A
Feb 196:11 PM
1
Notes.notebook
March 05, 2014
Find sine, cosine and tangent of each acute angle. Round to four decimal places.
C
sin A =
17
8
A
cos A =
B
tan A =
15
How are the acute angles related (Angles A and C)?
They are complementary
sin C =
Do you see any patterns with the sine and cosine of these angles?
cos C =
Yes The sine of one angle is the cosine of the other angle and vice versa.
tan C =
opp
hyp
adj
hyp
opp
opp
hyp
opp
adj
= .4706
sin A = .4706
= .8824
cos A = .8824
= .5333
tan A = .5333
= .8824
sin C = .8824
= .4706
cos C = .4706
= 1.875
tan C = 1.875
17
17
8
15
15
= hyp
8
15
= = adj
adj
= 17
8
= 17
15
= 8
Feb 196:11 PM
Find sine, cosine and tangent of each acute angle. Round to four decimal places.
X
sin X =
opp
hyp
= 4
= .8944
sin X = .8944
= .4472
cos X = .4472
= 2
tan X = 2
= .4472
sin Z = .4472
= .8944
cos Z = .8944
= .5
tan Z = .5
2√5
2√5
2
cos X =
Y
Z
tan X =
4
How are the acute angles related (Angles A and C)?
They are complementary
sin Z =
Do you see any patterns with the sine and cosine of these angles?
cos Z =
Yes The sine of one angle is the cosine of the other angle and vice versa.
tan Z =
adj
hyp
opp
adj
opp
hyp
adj
hyp
opp
adj
= = = = = 2
2√5
4
2
2
2√5
4
2√5
2
4
Feb 196:11 PM
2
Notes.notebook
March 05, 2014
Find sine, cosine, and tangent given the reference angle. Round to four decimal places.
sin 52º (Reference angle is 52º)
Calculator (Forward)
sin 5 2 =
Calculator (Backward)
5 2 sin =
sin 52º =.7880
Chart
Find 52º and then go to the "Sine" column
Feb 197:10 PM
Why does the Trigonometric Table and Calculator work for different sized triangles?
56º
34º
56º
34º
AA Similarity a right triangle with a given acute angle measure is similar to every other right triangle with the same acute angle measure.
Trigonometric ratios are constant for a given angle measure.
Why do you think you were asked to round to four decimal places earlier?
cot, csc, and sec will be covered in College Algebra/Trigonometry
Do you have any guesses as to what they are?
Feb 199:01 PM
3
Notes.notebook
March 05, 2014
Calculator Precision:
Angles can be measured in Degrees (DEG) and Radians (RAD).
Make sure your calculator is set appropriately (Mode: Degree)
Find sine, cosine, and tangent given the reference angle. Round to four decimal places.
cos 24º = .9135
tan 42º = .9004
sin 9º = .1564
tan 79º = 5.1446
Feb 199:07 PM
4

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