Transcript Sine and Cosine Ratios

Sec. 8 – 4
Sine and Cosine Ratios
Objectives:
1) To use sine and cosine to determine
side lengths in Δs.
2) To use the sin-1 and the cos-1 to solve
for  measures.
Just Buttons on the Calculator!
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Sine and Cosine are ratios of sides in a Right Δ.
Sin
Cos
The Sine and Cosine ratio in Rt. Δs
Sin  =
Oppisite Side
Hypotenuse
Cos  =
Adjacent Side
Hypotenuse
Hyp

Adjacent
Opposite
Write the Sin and Cos Ratio
Opp = 8
 Sin T =
17
Hyp
Adj = 15
 Cos T =
17
Hyp
Opp = 15
 Sin G = Hyp
17
Adj = 8
 Cos G =
17
Hyp
What do we call G and T?
G
Complementary
Interesting
T
17
8
15
For complementary s: Sin X = Cos Y
R
Ex.1: Solve for the missing variables.
Lets solve for x first.
6cm
x
y
Opp
Hyp
x
Sin 20 = 6
Sin 20 =
20°
Now solve for y.
Adj
Cos 20 = Hyp
(6)(.939) = y
y
5.6 = y
Cos 20 = 6
(6)(.342) = x
2.1 = x
The

-1
Sin
-1
Cos
and
-1
Tan
Use it when you are looking for missing s.
Use the shift (2nd) Key
Sin-1
Sin
Cos-1
Cos
Find the missing s
Any of the Trig ratios will work since you have all three sides.
Use the inverse sine ratio to solve for x.
y°
Sin x = 3.5
4.0
Sin x = .875
4.0
3.5
61° = x
Use the inverse cosine ratio to solve for y.
3.5
Cos y = 4.0
x°
1.9
Sin-1 (.875) = x
Cos y = .875
Cos-1 (.875) = y
29° = y
Pneumonic Device
djacent
pposite
angent
ypotenuse
pposite
ine
djacent
osine
ypotenuse
S =O H C =A H T = O A
SOH CAH TOA
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How do you know what trig ratio to use?
It depends on what is given to you and where
you are trying to go.
22°
15
x
x
40°
Cosine
55
Tangent
What have you learned??
Opposite
 Sin  = Hypotenuse
Adjacent
 Cos  =
Hypotenuse
Opposite
 Tan  =
Adjacent
** Use the Sin-1 and Cos-1 when looking for the 
measures.