Find the exact values of the six trigonometric functions of the given angle. Do
ID: 3026355 • Letter: F
Question
Find the exact values of the six trigonometric functions of the given angle. Do not use a calculator. -5 pi/4 Select the correct choice below and fill in any answer boxes within your choice. A. sin (-5 pi/4) = (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the B. The function value is not defined. Select the correct choice below and fill in any answer boxes within your choice. A. cos (-5 pi/4) = (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the B. The function value is not defined. Select the correct choice below and fill in any answer boxes within your choice. A. tan(-5 pi/4) = (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the B. The function value is not defined. Select the correct choice below and fill in any answer boxes within your choice.Explanation / Answer
We have given angle -5pi/4
sin(-5pi/4)=sin(-pi-pi/4)
=sin(-pi)cos(pi/4)-cos(-pi)sin(pi/4) since sin(A-B)=sinAcosB-cosAsinB
=-sin(pi)cos(pi/4)-cos(pi)sin(pi/4)
=0-(-1)*(1/sqrt(2)) since sin(pi)=0 and cos(pi)=-1,sin(pi/4)=1/sqrt(2)
=1/sqrt(2)
sin(-5pi/4)=1/sqrt(2)
cos(-5pi/4)=cos(-pi-pi/4)=cos(-pi)cos(pi/4)+sin(-pi)sin(pi/4) since cos(A-B)=cosAcosB+sinAsinB
=cos(pi)cos(pi/4)-sin(pi)sin(pi/4)
=(-1)*(1/sqrt(2))-0*1/sqrt(2)
=-1/sqrt(2)
cos(-5pi/4)=-1/sqrt(2)
tan(-5pi/4)=tan(-pi-pi/4)=[tan(-pi)-tan(pi/4)]/[1+tan(-pi)tan(pi/4)] since tan(A-B)=(tanA-tanB)/(1+tanAtanB)
=[-tan(pi)-tan(pi/4)]/[1-tan(pi)tan(pi/4)]
=[0-1]/[1-0*1] since tan(pi)=0 and tan(pi/4)=1
=-1
tan(-5pi/4)=-1
csc(-5pi/4)=1/sin(-5pi/4) =1/(1/sqrt(2)) =sqrt(2)
csc(-5pi/4)=sqrt(2)
sec(-5pi/4)=1/cos(-5pi/4) =1/(-1/sqrt(2))=-sqrt(2)
sec(-5pi/4)=-sqrt(2)
cot(-5pi/4)=1/tan(-5pi/4) =1/(-1)=-1
cot(-5pi/4)=-1