Trigonometry

1
Trigonometry
Chapter 6 Sections 16-20
Yeah!!!! We can use calculators!!!

• Measurement of triangles

2
Sine Cosine Tangent

• Sine, cosine and tangent are ratios that exist in
  right triangles.
• The ratio of two sides of any right triangle with
  the same interior angles is always the same
  number independent of the size of the triangle.
• They are abbreviated as Sin, Cos, and Tan

3
6
12
31
31
31
5
10
20
3
SOHCAHTOA

• Sin Opposite
• Hypotenuse
• Cos Adjacent
• Hypotenuse
• Tan Opposite
• Adjacent

4
SOHCAHTOA

• Sin A O
• H
• Cos A A
• H
• Tan A O
• A

A
H
5
3
A
C
B
O
4
5
SOHCAHTOA

• Sin A O
• H
• Cos A A
• H
• Tan A O
• A

• Sin B O
• H
• Cos B A
• H
• Tan B O
• A

A
5
H
3
O
C
B
A
4
What is the relationship between Sin A Cos B?
Tan A and Tan B ? Sin A Cos B b/c A B
are Cos A Sin B Complementary ?s Tan A
and Tan B are reciprocals.
6
page 771
Using the chart

• Examples
• sin 28 x
• cos 88 x
• Cos A .3746
• Sin B .6018

• Tan 31
• Tan 31

3
31
6
12
31
31
5
10
20
7
Using a calculator

• When you turn on your calculator ,
• check to see if Deg appears on the screen
• If not, hit button until Deg
  appears.
• To find the Sin, Cos, or Tan of any degree
  measure
• Find Sin 30 - Hit
• Sin 30 .5 or ½ - Hit
• Find Cos 30 - Hit
• Cos 30 .866025404 or
• We always round to 4 decimal places, so Cos 30
  .8660

DRG
3
0
SIN
3
0
COS
8
Using a calculator

• To show that tangents are reciprocals of each
• other using the calculator
• Find Tan 30
• You will get .577350269
• Take the reciprocal of this using
• You will get 1.73205080
• How do you find what angle this is the tangent of?

3
0
TAN
1/x
9
Do SOCAHTOA Tri Probs 2
10
Angle of Elevation

• READ PAGE 336

LINE OF SIGHT
ANGLE OF ELEVATION
HORIZONTAL LINE
11
Angle of Depression

• READ PAGE 336

HORIZONTAL LINE
ANGLE OF DEPRESSION
LINE OF SIGHT
12
Trig Word Problems
Steps

• Locate the ? in the problem
• Label sides according to the ?
• Decide which trig ratio to use
• Substitute
• Solve

13
Examples
1. From the top of a lighthouse 160 feet above
sea level, the angle of depression of a boat at
sea contains 35. Find to the nearest foot the
distance from the boat to the foot of the
lighthouse.
35
55
160
x
14
Examples
2. Find to the nearest degree the measure of the
angle of elevation of the sun when a vertical
pole 6 feet high casts a shadow 8 feet long.
6
x
8
15
Examples
3. A boy who is flying a kite lets out 300 feet
of string which makes an angle of 38 with the
ground. Assuming that the string is straight, how
high above the ground is the kite? Give your
answer to the nearest foot.
300
x
38
16
Examples
4. A plane took off from a field and rose at an
angle of 8 with the horizontal ground. Find to
the nearest ten feet the horizontal distance the
plane has covered when it has flown 2000 feet.
2000
x
8
17
Examples
5. A road is inclined 8 to the horizontal. Find
to the nearest hundred feet the distance one must
drive up this road to increase ones altitude
1000 feet.
18
Examples
6. A wire reaches from the top of a telephone
pole to a stake in the ground. The stake is 10
feet form the foot of the pole. The wire makes an
angle of 65 with the ground. Find to the nearest
foot the length of the wire.
19
Examples
A 40 feet ladder which is leaning against a wall
reaches the wall at a point 36 feet from the
ground. Find to the nearest degree the number of
degrees contained in the angle which the ladder
makes with the wall.