Download Identify the following trigonometric ratios

Identify the following trigonometric ratios.
77AA D
Deeffiinnee tthhee tthhrreeee ttrriiggoonnoom
meettrriicc rraattiiooss ((ssiinnee,, ccoossiinnee,, ttaannggeenntt)) iinn tteerrm
mss ooff aa rriigghhtt ttrriiaannggllee.
1. ____________= Opposite
Adjacent
2.
cos
= Opposite
________
3.
tan____=_________
Hypotenuse
Find the value of the trigonometric ratio for the following 2 problems and round to the nearest tenth.
77BB FFiinndd tthhee vvaalluuee ooff tthhee ttrriiggoonnoom
meettrriicc rraattiiooss ffoorr aa ggiivveenn aannggllee ooff aa ttrriiaannggllee..
4. sin C
5. tan A
Define the values of sin, cos, and tan for the following special right triangles
77C
C FFiinndd tthhee vvaalluueess ooff tthhee ttrriiggoonnoom
meettrriicc rraattiiooss ffoorr aa 3300ooo,, 4455ooo,, 6600ooo,, aanndd 9900oooaannggllee.
6. sin H=_____
cos K=_____
tan H=_____
7. sin F = _____
cos F = _____
tan F = _____
sin G = ____
cosG = ____
tan G = ____
Solve the following real world problems using trigonometric functions (determine what you have and
what you need).
77D
D SSoollvvee rreeaall w
woorrlldd pprroobblleem
mss iinnvvoollvviinngg iinnddiirreecctt m
meeaassuurreem
meenntt uussiinngg tthhee ttrriiggoonnoom
meettrriicc rraattiiooss..
8. A research vessel surveying the ocean floor for an ancient sunken Greek ship. The ship’s radar
sounded an object resting on the bottom of the ocean 900 feet diagonally from the ship’s hull. The
angle of depression from the ocean’s surface to the object is 45°. Determine how many feet the ship
must move forward to be located directly over the mystery object AND what is the depth of the object
from the ocean’s surface.
Using your trigonometry chart find the values of the sides or angles (value of variable “x”) of the
following problems, round to the nearest tenth.
77EE EExxppllaaiinn tthhee nnoottiioonn ooff aann iinnvveerrssee ttrriiggoonnoom
meettrriicc rraattiioo,, aanndd hhoow
w iitt iiss uusseedd ttoo ssoollvvee ttrriiggoonnoom
meettrriicc eeqquuaattiioonnss
77FF FFiinndd tthhee m
miissssiinngg ssiiddeess aanndd aanngglleess ooff aa ttrriiaannggllee uussiinngg tthhee ttrriiggoonnoom
meettrriicc rraattiiooss aanndd tthheeiirr iinnvveerrsseess..
9.
10.
12.
13.
11.
14.
Use the Pythagorean theorem to find the length of the missing side.
77II D
Deevveelloopp aanndd pprroovvee tthhee PPyytthhaaggoorreeaann iiddeennttiittyy..
15.
16.
17.
Use the tangent and the Pythagorean theorem to find missing lengths of the following equations (use
tan to solve for x first, then use Pythagorean theorem to solve for hypotenuse).
77JJ U
Ussee tthhee ttaannggeenntt iiddeennttiittyy aanndd tthhee PPyytthhaaggoorreeaann iiddeennttiittyy ttoo ssoollvvee ttrriiggoonnoom
meettrriicc eeqquuaattiioonnss..
18.
19.
20.