Suppose theta and phi are in the first quadrant and costheta

Suppose theta and phi are in the first quadrant and cos(theta) = 3/11 and tan(phi) = 13/5. Then determine the following cos(theta + 2 pi) = cos(theta - 2 pi) = cos(pi - theta) = tan(theta + 2 pi) tan(theta - pi) = tan(pi - theta) =

Solution

cos= 3_/11

=>sin=((11²-3²))_/11 =(112)_/11, tan=(112)_/3

cos( +2) =cos() =3_/11

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cos( -2) =cos() =3_/11

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cos(-) =cos()cos() +sin()sin()  

cos(-) =(-1)cos() +(0)sin()  

cos(-) =-cos()

cos(-) =-3_/11

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tan( +2) =tan() =(112)_/3

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tan( -) =(tan() -tan)_/(1+tantan)

tan( -) =(tan() -0)_/(1+tan*0)

tan( -) =(tan())_/(1+0)

tan( -) =tan()

tan( -) =(112)_/3

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tan(-) =(tan -tan())_/(1+tantan)

tan(-) =(0 -tan())_/(1+0*tan)

tan(-) =-tan()

tan(-) =-(112)_/3