Fall 2008 MAC 1114- Trigonometry Test #1 - Prof. Anna Wlodarczyk, Exams of Trigonometry

Download Fall 2008 MAC 1114- Trigonometry Test #1 - Prof. Anna Wlodarczyk and more Exams Trigonometry in PDF only on Docsity! Name: Fall 2008 MAC 1114- Trigonometry Test #1 There are 9 problems for a total of 100points. Show your work; an answer alone will get no credit. An illegible answer will not be graded. Any guessworkwill be disregarded. All answers must be simplified. Do not use a calculator Problem 1. (6 pts) a) Convert 50° into radians. Express the answer in terms of n. 51)° ~ 5J;(' if,gJi - ~\I- ~ g- \ b) Convert 8" into degrees 15 ~I~ ~iI- ~.~ \5- ~,F g'l~t=9GO Problem 2. (8 pts) Find the length of an arc subtended by the central angle of 70° in a circle with the radius 4 cm. Find the area of the sector subtended by that angle. ,b - 1--0q::: 10, Jj. = I1J;..v- \~O Ig 1. - - s- rrf) = ~.1JJ.. = ~- 1i'Q '1- 1Z.l{ A ::: 1('(:l. e ;:: 1 4 ~, !JL = 1. ~ , IlL '1 9v 2 , 8 % I 't8-4I 1f~4 ~ = 4 Problem 3. (8 pts) Find the exact value of the following expressions a) tan 60°cos 45° - cos 60°sin 60° b) sin 23°sec67° + tan 23° tan 67° ~11.fi. _J...lT3 v ~ ~"""i rra f3 ~J6- J3- -- - :...:...---- ~ 4 - Lt = Cosr'o11tJ~bfo +CO+b+~~bt.o \ j ~ CD~:{q. ~ + J- ~ ~-1° ~o ~61o =- l-tl~:L Problem 4 (10 pts) Draw the given angle in the standard position and find its reference angle a) 475° z ~600 + (\r' b) - 230° J.:: \~{/'- 'l5°; 65"° J=50° Problem 5. (20 pts) Use the reference angle to find the exact values of a) co{- 4;) = co+ (-4.00°) -= =: eo+( -:< 40Q) :=- eo+6 OK) - -L- - toM6O° - -1--- f3 - 13- 3 ,0 c) cos 300° ~ Cas 00 - I-- :L b) csc (570°) =:D;,G(?v60° t Q.lO) = -0 := - c.ou30 ---L. --1 -- ~1A?i)c- ,v d) sin(- 1~Jr) = ~111,t(- KlJ - ~IT)-4 4"- = ~\iw(-~U - ~'); =- ~'M. L--2>60°- t~s<') = - ~\I%4't' .::- :!3 .:L / Name: Fall 2008 MAC 1114- Trigonometry Test #1 There are 9 problems for a to'tal of 100 points. Show your work; an answer alone will get no credit. An illegible answer will not be graded. Any guesswork will be disregarded.All answers must be simplified. Do not use a calculator Problem 1. (6 pts) a) Convert 70° into radians. Express the answer in terms of 1t.0> .- --fll ~~ b) Convert 71Cinto degrees 12 J,r@"l-D =tlT !J( LWo- I 'l~~ 100/ ~~ ~;r_T P a "7/)0 .lJ... :to :: TV Jgoo Problem 2. (8 pts) Find the length of an arc subtended by the central angle of 40° in a circle with the radius 6 em. Find the area of the sector subtended by that angle. "'- - 40 ° 4 ~ iI ~iT AIY-/: CT - = \ ~j2f.:or ~ ) r, - Q @: s~ rr-e A-~..lrr'2.e 4 .l --" -- [)...,-. - .-A.I s= 4'~ -~ *~J..'62--~ _l.~.~ :=4\\q ~ C1 , ;).; <4 - ~ ~;t\ ~L Problem 3. (8 pts) Find the exact value of the following expressions a) cos600sin45° - sin 60° tan 30° b) cse37°sec53° - tan 53°cot 37° ::: =~~ ff:- ~w~ )..;;).. ~ ::>' rfi 3 - 3~- ~ - 1- ~ - l~ ~s~'03°'~5o0- +aM.53°.~63° ::- su,2iJ3<>- bwu,2.s-?>o= I Problem 4 (10 pts) Draw the given angle in the standard position and find its reference angle a) -105° b) 600° d-P cJ ~f~ (9000 ~ 060° + ;1..1\if' d:::'b rj=-{;oQ bOO'\) Problem 5. (20 pts) Use the reference angle to find the exact values of a) tan( - 7;):: ~ (-1'~O)~ ~ hvu L-2.1O'J ::=:- ~ oO{)JJt~: !r~ ,j;:;- - v3 .;> -- ~-~'O-O , r 0c) sin 300° ::::::: -4-\;1)\.,\0 0 ~~ ~-~ ~ b) sec (495°) C? SI<.C Vo60'o+ rOV\ :=::: - ~(.;4SO~~-0/ - __I - .::-~~ Cos4SO :::=> d) co{ _1:") = Cch (- l~~T - i:{) '> = CoSC - ~D - t[J = :::. Co~ ( - 6600-cl .10°) ~ - cos 30° = - J3 :7 ""V ~ --1J:h.6 Problem 6. (22 pts) Find the exact value of all trigonometric functions of an angle e given that a) seeB =-2, tan B > O. Use identities only. .7'-- ~ - e- ~ ~ qr~ fj1 CO~e =- -L .::: 1\!J <;ec17 Jv l @ ira12-e--t I= ~e ~'2.e + I;:: (-9.)1- 1.. 3 .. haM e::= ~r9- -: 173 (Ii) co+e~ L = ~~ ~ V -taMe % 3 (ffi ~ \J/ ~ 17- ~ -- <Z::Cose <mh'l ~;:f-aJU f1"Case:: '\13 . (~:0;;o -~ fA /,~pCL--L- ~-L--~ \2/ ~.:>v v-- <b1~tr ~ - 2;- b) sin B =~, cot B < 0 ~ ! - e Vt\ JL cr- I b... 3 ~11te-:; ;y:: ..., 4" J ~ ~?J /1=4 ~ :; -tf&"L :: -fI6=Ot=-ffttr LJ ~ce-= b ~ 3 Q, - -fi. Cos e-:: ry::-- '-I rY'- 4 ...- ill ~<g- =- a.- ~ -~ - =f- I, ,Q.- ~ - . -2 --ill ~ V --- GU- -1$- ::p I ,Q.. -: g.. ~- -Ii Co+-v (0- 3