Question

Evaluate the following without using the calculator


`\cos(30) \sin( (\pi)/(4) ) + ( \sec(60) )/(3)`

Answer 1

`\sec x=(1)/(\cos x)\to \sec60^o=(1)/(\cos60^o)\\\\\text{Use the table of values of a trigonometric functions}\\\\\cos30^o=(\sqrt3)/(2)\\\\\sin(\pi)/(4)=(\sqrt2)/(2)\\\\\cos60^o=(1)/(2)\to\sec60^o=(1)/((1)/(2))=2\\\\\text{Substitute:}\\\\\cos30^o\sin(\pi)/(4)+(\sec60^o)/(3)=(\sqrt3)/(2)\cdot(\sqrt2)/(2)+(2)/(3)=(\sqrt6)/(4)+(2)/(3)\\\\=(3\sqrt6)/(3\cdot4)+(4\cdot2)/(4\cdot3)=(3\sqrt6)/(12)+(8)/(12)\\\\=\boxed{(8+3\sqrt6)/(12)}`