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Click here to check out ALL problems on Trigonometry-basicsQuestion 1157805: express cos241 as a role of a confident acute angle. discovered 2 solutions by Edwin McCravy, Shin123:Answer by Edwin McCravy(18936)
(Show Source): You have the right to put this systems on her website! 241° is in between 180° and 270° i beg your pardon is the 3rd quadrant, QIII. That"sthe reduced left quadrant. 241° has this terminal side and also the red arcshows its counter-clockwise rotation from the right had actually side that the x-axis. An alert that 241° is consisted of of 2 angles the rotation. The 180° rotation (in green) and also the rotation after 180° which is 241°-180° = 61° (in blue):So the angle shown by the blue arc, between the x-axis and the terminalside is 61°, and we say that "the referral angle that 241° is 61°". ThisREFERENCE angle has actually the exact same sine, cosine, and also tangent together 241² other than fortheir hopeful and an adverse signs. Now find out the sentence: "All Students take it Calculus" come remember "All S T C"For the quadrants, think of this together though it to be an x,y name: coordinates system: S|A T|CThe significant three trig functions are Sine, Cosine, and Tangent, the othersare their reciprocals. This memory maker only works v the significant threetrig functions, Sine, Cosine and Tangent."All" reminds united state that all trig attributes are hopeful in the very first quadrant QI."STUDENTS" reminds us that of the significant three trig functions, the SINE isPOSITIVE in the second quadrant QII, and the various other two significant trig functions areNEGATIVE there."TAKE" reminds us that that the significant three trig functions, the TANGENT isPOSITIVE in the 3rd quadrant QIII, and the various other two major trig features areNEGATIVE there."CALCULUS" reminds united state that of the major three trig functions, the COSINE isPOSITIVE in the fourth quadrant QIV, and also the various other two major trig functions areNEGATIVE there.If the significant trig function, the SINE, is confident or an unfavorable in a quadrant, itsreciprocal, the COSECANT is additionally positive or an adverse there.If the significant trig function, the COSINE, is confident or negative in a quadrant,its reciprocal, the SECANT is also positive or an unfavorable there.If the major trig function, the TANGENT, is hopeful or negative in a quadrant,its reciprocal, the COTANGENT is additionally positive or an unfavorable there.Now if we have actually learned that, let"s go with what this details tells usabout the positive-ness or negative-ness of cos(241°).The cosine is an adverse in the 3rd quadrant, QIII. Yet the cosine of thereference edge is always positive, because if place in appropriate position itwould always be in the first quadrant QI wherein all trig rations and functionsare positive. For this reason to acquire the answer to this problem, simply put a negativein prior of cos(61°) and also that"s her answer:Answer: cos(241°) = -cos(61°)Edwin prize by Shin123(544) (Show Source): You can put this equipment on her website! First, using the truth that , plugging in 241o for theta gives . Next, making use of the identity offers .
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Splitting by -1 offers .