Can someone help me with this add maths multiple choice question?

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2 Answers
Jim G.
Jun 4, 2018

#x=35^@to(A)#

Explanation:

#"using the "color(blue)"cofunction identity"#

#•color(white)(x)cos(90-x)=sinx#

#cosx=cos(90-(x+20))=cos(70-x)#

#"thus "x=70-xrArr2x=70rArrx=35^@#

#"that is "sin55^@=cos35^@#

Ben
Jun 4, 2018

The answer is (a)

Explanation:

We can figure this out by first eliminating the choices that don't make sense.

(b) can't be the answer because if #x=45^@#, then #sin(x)=cos(x)# because #sin(45^@)=cos(45^@)#. Therefore, #sin(65)!=cos(45)#

(d) also cannot be the answer, because #sin(90)=1#, and #cos(70)!=1#

This leaves us with (a) and (c) for options.

If you plot #sin(x)# and #cos(x)#, you find that #sin(x)# is increasing as #xrarr90^@# and #cos(x)# is decreasing. since we know that #sin(45^@)=cos(45^@)#, It would stand to make sense that the answer should have #45^@# as a halfway mark between the evaluated answers.

graph{(y-sin((pix)/180))(y-cos((pix)/180))=0 [-90, 180, -.5, 1.5]}

Taking the average for option (a):

#(35+55)/2=90/2=45#

This looks good, lets check option (c):

#(55+75)/2=130/2=65#

This doesn't sit over 45, so our best bet is to go with option (a).

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