Study Guide: Trig Functions
Topics:
Sin <t:
Name - - - - - - - - -
1. Angles of a right triangle
2. Geometry Concepts: Complementary angles, Supplementary angles,
Vertical angles, Alternate Interior angles, and Adjacent angles
3. Pythagorean Theorem and Pythagorean Triples
4. Right Triangle Trigonometry
• Using sin, cos, tan to calc missing sides
• Using sin- J , cos-], tan-] to calc missing angles
5. Word Problems - including angle of elevation & angle of depression
=
Opposite
Hypotenuse
Cos <t:
Adjacent
Hypotenuse
Tan <t:
= Opposite
Adjacent
Angle of Depression and Elevation
The angle of depression to an object is the angle formed between the horizontal line of
sight and the actual line of sight to an object below.
B ---------,--~_=_-;---...,.--_r­
Angle of depression
Angle of elevation
The angle of elevation to the top of an object is the angle formed between the horizontal
line of sight and the actual line of sight to an object above.
Practice:
1. Find the angle of LA
2. Find the angle of LB
12~
3. Find the lengths of the sides (x andy) in the following triangles
70°
x
t·­
24
y
8
4. Set up appropriate trig equations and solve the following word problems
a.
A boat. lost in the fog of the ocean, can see the light at the top ofa 70-foot light­
tower. If the boat is actually 1000 teet away, at what angle did the captain sea the
light on the light-tower?
b.
Tom is flying a kite at the beach and has let out all 100' feet of string. If the kite is
flying at an angle of elevation of60° , how high off the ground is the kite.
c.
A person is hiking on a path 300 feet above a lake. The hiker can spot his friend
fishing in a boat on the lake at an angle of depression of 40° , how tar (horizontally)
apart are they?
Name~
Study Guide: Trig Functions
Topics:
Sin
<l: =
_
1. Angles of a right triangle
2. Geometry Concepts: Complementary angles, Supplementary angles,
Vertical angles, Alternate Interior angles, and Adjacent angles
3. Pythagorean Theorem and Pythagorean Triples
4. Right Triangle Trigonometry
• Using sin, cos, tan to calc missing sides
• Using sin- J, cos-J , tan- J to calc missing angles
5. Word Problems - including angle of elevation & angle of depression
Opposite
Hypotenuse
Cos
Adjacent
<l:
Hypotenuse
Tan
<l: =
Opposite
---­
Acijacent
Angle of Depression and Elevation
The angle of depression to an object is the angle formed between the horizontal line of
sight and the actual line of sight to an object below.
B-------:---c:-:-----:--~Angle of depression
on"'\.
~,(\e
0\ s''''
Angle of elevation
The angle of elevation to the top of an object is the angle formed between the horizontal
line of sight and the actual line of sight to an object above.
Practice:
1. Find the angle of 4A
I"Y)LA ~
k> I 0
2. Find the angle of 4.-B
12
~
cosA
~ fh.
;Ls
mL A= cos -I
(12/2~) ~ h 1..3
-tctnB-=~
(nL(6 -=
+M-(( )'2../s) ~ G1·Lt
3. Find the lengths of the sides (x andy) in the following triangles
Sin ,0'> -::
70°
I
21
)(
X, Sin,o -= dLt
Si(\IQ
5'1(\10
X = ~tf
24 o~p
~~:;;t()lO D
/V
rv
"5 ~
d
,j
yo..
8
Opp
4. Set up appropriate trig equations and solve the following word problems
a.
A boat, lost in the fog of the ocean, can see the light at the top of a 70-foot ~t­
tower. Ifthe boat is actually 1000 feet a\vay, at what angle did the captain ~the
light on the light-tower?
+etn e~ 7o~o
10
{-to
IOOO~t
b.
.:;~,
,~>.
e
=
-fun-I (lOll 000)
4
~
I~~ ~~ Ol'QkJl- ~Q. yoo~:\)
r'1'~'~,
Tom is flying a kite at the beach and has let out all 100' feet of string. If the kite is
flying at an angle of elevation of60° , how high off the ground is the kite.
Sin t:J:l-:: L
100
.
X = I 00 s ;n bO°
x
t.i ···
f>::,
~.la
~~~
I
·.~
<~
c.
.
I.'.:.;...•·.'.·.·. . . ·
It
A person is hiking on a path 300 feet above a lake. The hiker can spot his friend
0
x
fishing in a boat on the lake at ao angle of depression of 40
apart are they?
0
ii'
-
4a:J - - - -
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{t
t.)(
boot-
•
how far (horizontaUy)
+M YOL' = 300
-fa.nSOo = L
300
X ~ 3CO ian S- (j'
o'
':::
.T\\.e ~ evrJ
3<;'7.<;
f0,
i"ce;,.j
300 X
'X - +o.n '-10°
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3 '5'7. S"
r
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