Transcript 7.4 Trigonometry

7.4 Trigonometry
What you’ll learn:
1. To find trig ratios using right
triangles.
2. To solve problems using trig
ratios.
Trigonometry
• Trigonometry – the study of triangle
measurement
• Trigonometric Ratio – the ratio of the lengths
of sides of a right triangle.
• Three most common trig ratios – sine, cosine,
and tangent.
• Trig ratios are related to the acute angles of a
right triangle, never the right angle.
Sine ratio
A
b
C
c
a
B
Opposite
sin of A=
or
Hypotenuse
Opposite
sin of B=
Hypotenuse
a
c
b
or
c
Cosine Ratio
A
b
C
c
a
B
b
c
a
or
c
Adjacent
cos of A=
or
Hypotenuse
Adjacent
cos of B=
Hypotenuse
A
b
C
c
Tangent Ratio
a
Opposite
tan of A= Adjacent
B
a
or
b
Opposite
tan of B=
or
Adjacent
b
a
Writing Ratios
Find sin A, cos A, tan A, sin B, cos B, tan B. Express
each ratio as a fraction and as a decimal to the
nearest hundredth.
8
15
15
sin A=
cos A=
tan A=
17
8
17
17
sin B=
8
17
15
cos B=
17
15
8
tan B=
15
A
8
C
Using the calculator
Scientific calculators are programmed to know what
the ratios will be for all angles. You can enter the
angle and it will give you the ratio (as a decimal) or
you can enter the ratio and it will give you the
angle. Since we are dealing only with degrees, make
sure your calculator is in “degree” mode (D or DEG
should be visible)
When you are given the angle:
Example: sin 50
(enter sin 50 then press enter or enter 50 and press
sin)
0.7660
When you are given the ratio:
To find the angle from a ratio, you must use the
“second” or “shift” key to find it. (use cos 1
etc..)
Ex: cos X=0.8734
Enter Shift cos 0.8734 then enter or 0.8734 and
shift cos
X=29.14
Finding Missing Parts. Find x to the
nearest tenth.
1.
14
x
3.
x
16
46
32
4.
2.
18
x
X
7.5
9
15
Homework
p. 368
18-48 even