Sec' 8 4 Sine and Cosine Ratios

1
Sec. 8 4Sine and Cosine Ratios

• Objectives
• 1) To use sine and cosine to determine side
  lengths in ?s.
• 2) To use the sin-1 and the cos-1 to solve for
  ? measures.

2
Just Buttons on the Calculator!

• Sine and Cosine are ratios of sides in a Right ?.

Sin
Cos
3
The Sine and Cosine ratio in Rt. ?s
Oppisite Side
Sin ?
Hypotenuse
Adjacent Side
Cos ?
Hypotenuse
Hyp
Opposite
?
Adjacent
4
Write the Sin and Cos Ratio
8
Opp

• Sin T
• Cos T
• Sin G
• Cos G

What do we call ?G and ?T? Complementary
17
Hyp
G
15
Adj

17
Hyp
Interesting
17
15
Opp
8

17
Hyp
8
Adj
R
T

15
17
Hyp
For complementary ?s Sin X Cos Y
5
Ex.1 Solve for the missing variables.
Lets solve for x first.
Opp
6cm
Sin 20
Hyp
x
x
Sin 20
20
6
y
(6)(.342) x 2.1 x
Now solve for y.
Adj
Cos 20
Hyp
(6)(.939) y 5.6 y
y
Cos 20
6
6
The Sin-1 and Cos-1

• Use it when you are looking for missing ?s.

Use the shift (2nd) Key
Sin-1
Cos-1
Sin
Cos
7
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
3.5
Sin x
4.0
Sin-1 (.875) x 61 x
Sin x .875
4.0
Easier Way?
Use the inverse cosine ratio to solve for y.
3.5
3.5
Cos y
4.0
Cos-1 (.875) y 29 y
x
Cos y .875
1.9
8
Pneumonic Device
S O H C A H T O A



ine
angent
djacent
pposite
osine
ypotenuse
ypotenuse
pposite
djacent
9

• 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
x
x
15
40
55
Cosine
Tangent
10
What have you learned??

• Sin ?
• Cos ?

Opposite
Hypotenuse
Adjacent
Hypotenuse
Page 441 1-28 all
Use the Sin-1 and Cos-1 when looking for the
? measures.