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Sec. 8 – 4 Sine and Cosine Ratios. Objectives: 1) To use sine and cosine to determine side lengths in Δ s. 2) To use the sin -1 and the cos -1 to solve for measures. Just Buttons on the Calculator!. Sine and Cosine are ratios of sides in a Right Δ. Sin. Cos. - PowerPoint PPT Presentation
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Sec. 8 – 4Sec. 8 – 4Sine and Cosine Sine and Cosine
RatiosRatiosObjectives: Objectives:
1) To use sine and cosine to 1) To use sine and cosine to determine determine side lengths in side lengths in ΔΔs.s.
2) To use the2) To use the sinsin-1-1 and the cos and the cos-1-1 to solve to solve for for measures. measures.
Just Buttons on the Just Buttons on the Calculator!Calculator!
Sine and Cosine are ratios of sides in Sine and Cosine are ratios of sides in a Right a Right ΔΔ..
CosCosSiSinn
The Sine and Cosine ratio The Sine and Cosine ratio in Rt. in Rt. ΔΔss
Sin = Oppisite SideHypotenuse
Cos = Adjacent SideHypotenuse
Hyp
Opposite
Adjacent
Write the Sin and Cos Write the Sin and Cos RatioRatio
Sin T =Sin T =
Cos T = Cos T =
Sin G =Sin G =
Cos G =Cos G = T R
G
17 8
15
OppHyp
= 817
AdjHyp
= 1517
OppHyp
= 1517
AdjHyp
= 817
What do we call G and T?
Complementary
For complementary s: Sin X = Cos Y
Interesting
Ex.1: Solve for the missing Ex.1: Solve for the missing variables.variables.
20°
xx
yy
6cm
Lets solve for x first.
Sin 20 =OppHyp
Sin 20 = x6
(6)(.342) = x
2.1 = x
Now solve for y.
Cos 20 = AdjHyp
Cos 20 = y6
(6)(.939) = y
5.6 = y
The SinThe Sin-1-1 Cos Cos-1-1 and Tan and Tan-1-1
Use it when you are looking for Use it when you are looking for missing missing s.s.
CosSin
Sin-1 Cos-1
Use the shift (2nd) Key
Find the missing Find the missing ss
x°
y°
1.9
3.5
4.0
Any of the Trig ratios will work since you have all three sides.
Use the inverse sine ratio to solve for x.
Sin x =
3.54.0
Sin x = .875
Sin-1 (.875) = x
61° = x
Cos y =
3.54.0
Cos y = .875
Cos-1 (.875) = y
29° = y
Use the inverse cosine ratio to solve for y.
Pneumonic DevicePneumonic Device
S O H C A H T O A
ine pp
osite
ypote
nu
se osin
ed
jace
nt
ypote
nu
se
an
ge
nt
pp
osit
e dja
cen
t= = =
SOH CAH TOA
How do you know what trig ratio to How do you know what trig ratio to use?use?
It depends on what is given to you and It depends on what is given to you and where you are trying to go.where you are trying to go.
15
22°
x
Cosine55
40°
x
Tangent
What have you learned??What have you learned??
Sin Sin = =
Cos Cos = =
Tan Tan = =
OppositeHypotenu
seAdjacentHypotenu
se
** Use the Sin-1 and Cos-1 when looking for the measures.
OppositeAdjacent
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