Math 148 - 001 - 002EXAM 3 Name:Dr. P.D. McCray 22 November2006Whenradicalsappearin ananswer,leave theanswerin thatform ratherthan usinf!a calculator.1. (5 points each)(a) If the angle a measures 1950, what does a measure in radians? EXDressyour answer in terms of 1r./O::-7T ~'~ 1957T_(137T/12~'~I~() /~O -(b) If the angle fJ measures 11:rrradians, what does fJ measure in degrees?12 00/ ~~ ~ I&'9 .JO~d~~ I/TT, 10-7/ ---q ~ /2. 7r2. (12 points) Use the information that sin () = 24 to find the values of the remaining five trigonometric25functions of (), assuming that the angle ()is acute.~~ "- +-/~J.)'"L.:: I'1...\..:z.~'2.._I'2..~'l ..,)"2-1C - ---z.~'2.: 'l..1\'2..-:: 2 9 -2... Y.z.g'L...,.2.-(;1.fj - 2" )(2.5 +1-'1)1.. +'1 "2~2. 7--~ :. ~-z... ~X::. ~Express each of the following in terms of cos a, sin a, cos fJ, sin fJ.3. (6 points each)(a) cos(a + fJ) =(b) sin(a + fJ) =zY-l.5(c) sin(2a) =Math 148 - 001 - 002 EXAM3Name:Dr. P.D. McCray 22November20064. (7 pointseach) Supposethat sinO= -1/4 and n < 0 < 3n/2.......(a) Find cosO -= - ~ 0{ -:::(- -L ~'2- 11... '2.. \. Jf1( t- G) = f'2-I I~---1' --=-I - .-L--=-_lIP t(P71 -: i<~I~ !. {j5- -= e;r,7 0(I~ IfPage 2 of 4(b) Find csc0 and cot0~ 6Z-= / ::: I .::~~ b -1/4 '--J~(}:: epof7' ==- ~/t-. ::: (v.'I~~ f!J - 1/4..(d) Find cos(O+ n/3) :=. ~(O{ i--(3) -::. ~o( C()::1fJ - ~ 0( ~ft0( :: 9/ f3 = 0/3U/?(Y+7T/3)-= ~e ~~-~e~J'~ (-'J){{) -(-i)(Y{)~(e+-%)::: .¥3- ~'3Dr. P.D. McCray 22November20065. (7 points) Provethat csce - cot e= 1cot e+ csc - .L HS = I _ Ce?<Jt7 -::: I - ~t9 I 1- ~6-#~ fJ AANJ (;. ~ f7 I T- ~f7_ I - C-dJ'2(). ~ '<&..-. -:.~ {;>-(/+~8} ~ f7-(I1-~tJ-)_ ~ f/- '~f:j' I. . ~I+-~(? '~ f7Math 148 - 001 - 002 EXAM 3Page 3 of 4Name:I-- .,.=-RtfSCAfk (;) + ee:f (:J~ Z:4...t Il_ klJ ,,~.. Il -/v1 tr"Vf 4-A'tlU. ...J-~ ~ A.-t...C£t>~ L.P .") ~~~~~,6. (7 points) Sketch the graph of y = tan Jrx for 0 :::x :::1.'If"/i''Z-{3{{(I( ~,..I If'0-,--,----I,Lf-_'2..Math 148 - 001 - 002Dr. P.D. McCray7. (6 points each)EXAM 3 Name:22 November 2006Page 4 of 4(a) What is the periodof y = f(x) = 2cos:rrx?Tk-€-~\vzf'*I rY ~ A- ~~;r", c ) ~<2rr/ I?) ~ ;;I.7T'/ 7T ==-0(b) Sketch one complete cycle of the graph of y = 2cos:rrx.1-.'l--,-'2-(c) Find all solutions of the equation 2cos :rrx = 2 forx in the interval 0 ::::x < 2:rr.~ ~ 7J7< -::. ~ ~ ~?r-?( -:::./~ '1- -=-/ ~;,n 'J::=-0 In 0:5 if- < 37r~~" ;? ~-n-x ~ ~ ~ ~~'t1>'V:J ~ ~~ ~ :t =: () ~02.~1~~~~~.7T-X ~:t '::::+-2 TT~ ="/ 71 ¥27rk. -:. ~;?~~ ~7IZ (,.23.J~~~~ -?(#-.d-~' ~~~-X:: 0 I .2 , 41 ~ ~ ~ (J~ :x ~
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