Transcript TRIG2

Trigonometry
http://www.youtube.com/watch?
v=t2uPYYLH4Zo
Trigonometric Ratios
There exists a ratio of side lengths of a right triangle which is
the same for all similar triangles.
Ex. The ratio of
short _ leg
hypotenuse
of a 20-70-90 triangle
is the same for all 20-70-90 triangles.
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TRIGONOMETRY
Greek word meaning “measurement of triangles”
Three Basic Trig Ratios
hypotenuse
c
A
B
a Side
opposite A
C
b
Side adjacent to A
side Opposite A (a)
Sine A (Sin A) =
Hypotenuse
(c)
Cosine A (Cos A) =
side Adjacent A (b)
Hypotenuse
(c)
side Opposite A (a)
Tangent A (Tan A) =
side Adjacent A (b))
Meet My Friend
SOH CAH TOA
Sine
Cosine
Tangent
Opposite
Adjacent Opposite
Hypotenuse Hypotenuse Adjacent
Finding Trig Ratios
E
14
F
50
48
Find Sin, Cos and Tan of D and E
** Round to nearest ten-thousandths
D
14
SinD = 50 = 0.28
48
CosD = 50 = 0.96
14
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TanD = 48 = 0.2917
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48
SinE = 50= 0.96
14
CosE = 50 = 0.28
48
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TanE = 14 = 3.4286
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Which ones are the same? Why?
Finding Trig Ratios 2
Check out Examples 1 and 2 on pages 558-559
 Does the size of the right triangle matter in Ex. 1?
 What is the determining factor for the trig ratio?
Check out Examples 3 and 4 on pages 559-560
 What is true about the sin 45o and cos 45o?
 Why is the tan 45o = 1?
 If the sin 30o = 0.5, then what is cos 60o?
Using Trig Ratios in Real-Life
You can use trig ratios to calculate
heights or distances.
FIRST - you need to be able to find the sin, cos or tan of an angle.
Put Calculator into DEGREE mode:
Press MODE - make sure DEGREE, not RADIAN is
highlighted
Find sin 36o - you should have gotten 0.5878
Find tan 53o - you should have gotten 1.3270
Trigonometry
Trigonometry
Using Trig Ratios in Real-Life
Find the height of a building:
You stand 100 ft. from the base of the building, the angle of
elevation = 48 from a point on the ground to the top of the
building.
Pretend you’re standing
at the angle.
h
48o
100 ft.
What trig ratio uses opposite and adjacent? Tangent!
tan 48o = h(opp)
=> 100(tan48o)= h
100(adj)
100(1.1106) = approx 111 feet
Using Trig Ratios in Real-Life
Check out Examples 6 and 7 on page 561.
Angle of Elevation = Angle formed by your line of sight
from the horizontal upward.
Angle of Depression = Angle formed by your line of sight
from the horizontal downward.