Trig Quiz 2, Spring 2021
Show all your work and circle your final answers! Questions are 10 points each unless stated otherwise.
1.
(8pts) Use the cofunction identities to fill in the blanks
--IT 11
n:)
.
jl. - ,cos (5 = sin( "L
5'
a)
b) tan(l0° - 2x)
2.
) = sin (
~'~0__)
:m
= cot(_ct_o"_---'-(-~---~_)_ _ _ _ _ _) = cot( i~ +7...y..
)
(12 pts) Use the figure below to evaluate the six trigonometric functions for angle 0. Show all work, simplify all
fractions and rationalize the denom;nato,s ;f needed, 1;,t yo"' final TwT below the fig"'•·
0\.,.. +11;)'2..::,c_~
s,~(~)= 2££.
~to)~~
CA"t • -r."'-: i'I..
"''4P
!
~p
4
'-"-'"... ~-8>c0Dl• ~---u
:::.m
l::[J
=
kteJ,
C~t,(~::
o.::~
3
.! . .f! ~@ -Stt(&) ..fIJ
Ji
C.C1-t&) -:
Y.5
t!1
,rs
"2.,li
'i':~
:00
-cr}
2
sin(0)
= .f-s
csc(0)
=
cos(0)
=
sec(0)
=~
cot(0)
= "'--fi?
tan(0)
3.
3
= ..fs-z_~
s
"Z..
A radio tower is located 320 ft from the building. From a window in the building a person determines that the
angle of elevation to the top of the tower is 44°, and the angle of depression to the bottom of the tower is 35°.
How tall is the tower?
\
w,,.. (
3s0 J
~"iu
'I<
= 3 '!.D + -\.cw,. t ?."'S)
-z_""Z...~ .Ofc,~~
I
'3U),,\;c:.M. l44°)-:.
= &oc, .0'2..
y...
· 5ro
"LJ-\ .O(a ::!\S~~ .Ot (;~
-1r "Z..
1
- ----- - - ---•n"'"•_...,..,.,.,n_,..__lllllllll...,,.OMJU-1--IMIT!IIJ__ ____
.,.fl.,..,,,____..,~-~iu.ruo,i-•!11-- -
m,,_«'1.fln•••"'"'"'";v"""'
4. Assuming that a 27O-foot tall giant redwood grows vertically, if I walk a certain
distance from the tree and measure the angle of elevat ion to the top of the tree to be
55°, how far from the base of the tree am 17 Round your answer to the nearest foot.
t&w\.. l-sr;-~) ";'. .
-=-
"'?-.,o
"T-.t~0)
5.
Use the Pythagorean identity to find cos (0) if sin(0)
C..osq_ Q - ~,V\-z... Q -=- l
L0'5'?.. Q -
C...0~'""&) -
l- 'l4)
°'l11o-::.
C..,o~-z..Q -:::: \ + ~,,
f"c..o~ 7..~ ·~ J"-'S
----
-=- [ \~9 . 0 ~
= - 4 and the terminal side of 9 is in quadrant 111.
hmm..you should really work on the quizzes and exams
individually, same mistakes are grounds for cheating
investigation.
:: \
I
t\lo
l!o
+.9..
\Co
6. (15 pts) The terminal side of an angle 0 passes through the point ( ...ff. -3). Calculate exactly
the values of the cos(0), csc(0) and tan(0) trigonometric functions of 8. Simplify all answers,
rationalize the denominators if needed.
r,
~-3
u...7.. + 'v:::,'t. = C,
{fi)" ;-~3)~= c<, + C\::
,ffi, -=-Jc:
c..-= 4
(,<..
'l_
7. Use identities to rewrite the expression as a single trigonometric function.
\
csc (t)
b)
-=
sec (t)
~
~l-lo)
-l\)
\
l
8. Answer the following questions:
a) If cos(0) =½,then cos(-0) =
-=-i~'1J
Ce>s l-fs) -= - ~(~)
b) If sin(0) = 0.657, then sin(-0) =
:=f- O. Cos~
-5,\1\. (.~)
c) If tan(0) =~'then tan(-0) = - -k,,. tS)
=\
-~J
9. (15 pts) Use the appropriate identities to find sin(0) and cos(0), if tan(0) = 2 and the
terminal side of 0 is in quadrant Ill. Rationalize denominators when necessary.
-z..o • \ = o~c.. e
CW\
-z....
( -Z..) -+ I -::
<Sc.<.e :
"Z..
5 <.'--z..
4 + \ :. s ~(.,"t.
\;: /
-G =~S.u.'<9
~d..~) =rsBonus: (5 pts, no partial credit) .
0'1°
MQ
~,:,-----.
.
rr-~--8-=-----:::=~;-,l
{s°:: .l_
r __ " _
:
I
.fs-
,J'S"
~-\,\.~e
"'"~-z..Q
~""'?..e~ (JiJ-.
'
'S ...~ 9 •
" I
.
\
[
,fs
-
·· -s
~l\.\.7-e; \-l. -~ s
r:;:-~
r.t -s
-s
\)"'b\t\ Q-:'1'$
5,,.._ El
.,_-'5!]
.... l.
simplify
-s
.
A 400-foot tall monument is located in the distance. From a window m the build mg, a person determines that
the angle of elevation to the top of the monument is 25°, and that the angle of depression to the bottom of
the monument is 7° . How far is the person from the monument?