Download 8-3 the Tangent Ratio 8-4 the Sine and Cosine Ratio

8-3 the Tangent Ratio
8-4 the Sine and Cosine Ratio
California Standards
18 Students know the definitions of the
basic trigonometric functions defined by the
angles of a right triangle.
19 Students use trigonometric functions to
solve for an unknown length of a side of a
right triangle, given an angle and a length
of a side
Trigonometric Ratio Activity
• Select one angle measure from 10o through
80o.
• Use a protractor, draw the selected angle.
Label the angle A.
• Draw a right triangle ABC.
• Measure each sides of the triangle to the
nearest mm.
BC BC AC
Compute the ratio
,
,
.
AC AB AB
•
•
•
•
•
hypotenuse
leg
to A
A
Adjacent leg
•
C
C
leg
Opposite
opposite
A
leg adjacent to A
B
B
• Extend AC and AB.
• Draw 2 more right triangles AB1C1 and
AB2C2 as shown below.
c2
•
c1
•
C
•
A
B
B1
B2
Results
• .
Triangle
opposite
hypotenuse
adjacent
hypotenuse
1

2
3


opposite
adjacent
Make a Conjecture.
opposite leg
adjacent leg
The ratio
is constant
no matter the size of the right
triangle.

This trigonometric ratio is
called the tangent ratio.
Trigonometric ratios
opposite leg
hypotenuse
• With a given angle the ratio
is
always a constant number.
• This ratio is also known as a sine ratio.
adjacent leg
• Similarly the ratio hypotenuse is known
as the cosine ratio.

Classwork
• Page 434 # 4 - 16 even
• Page 441 # 4 - 16 even
• Homework:
• Page 450 # 1- 7