Download Lesson 8-4 Trigonometry with answers.notebook

Lesson 8­4 Trigonometry with answers.notebook
February 18, 2015
Questions/Main Ideas Lesson 8­4 Trigonometry
trigonometry ­ from Greek, trigon, meaning triangle, and metron , meaning measure
Trigonometric Ratios
words:
sine A = measure of leg opposite A
measure of hypotenuse
B
sin A = BC
AB
opposite A
sin B = AC
AB
A
C
opposite B
Questions/Main Ideas
words:
cosine A = measure of leg adjacent A
measure of hypotenuse
B
cos A = AC
AB
adjacent to B
C
cos B = BC
AB
adjacent to A
A
1
Lesson 8­4 Trigonometry with answers.notebook
February 18, 2015
Questions/Main Ideas
words:
tangent A = measure of leg opposite A
measure of leg adjacent A
B
tan A = BC
AC
adjacent to B
and opposite to A
tan B = AC
BC
A
C
adjacent to A
and opposite B
Questions/Main Ideas mnemonic device
SOH ­ CAH ­ TOA
co
ta
n s =
=
o
ad
h= op
p
h
yp jac
ad pos
yp po
e
s
o
ot ite
jac ite
ten nt en e
sin
us e
us
e
nt
Example 1
Find sin L, cos L, tan L, sin N, cos N, and tan N. Express each ratio as a fraction and as a decimal.
2
Lesson 8­4 Trigonometry with answers.notebook
February 18, 2015
Questions/Main Ideas Example 2
Use a special right triangle to express the cosine of 60 as a fraction and as a decimal to the nearest hundredth.
Example 3
Find each value to the nearest ten thousandth (be sure calculator is in degree mode)
a.
tan 56
b.
cos 89
Questions/Main Ideas Example 4
A fitness trainer sets the incline on a treadmill to 7 degrees. The walking surface is 5 feet long. Approximately how many inches did the trainer raise the end of the treadmill from the floor?
3
Lesson 8­4 Trigonometry with answers.notebook
February 18, 2015
Questions/Main Ideas Find the measure of an angle by using the inverse of sine, cosine, or tangent.
4
Lesson 8­4 Trigonometry with answers.notebook
February 18, 2015
Questions/Main Ideas Example 5
Use a calculator to find the measure of P to the nearest tenth. Questions/Main Ideas solving a right triangle ­ finding all of the missing sides and angles
you must know two side lengths or
one side length and the measure of one acute angle
Example 6
Solve the right triangle. Round side measures to the nearest hundredth and angle measures to the nearest degree.
5
Lesson 8­4 Trigonometry with answers.notebook
February 18, 2015
6