Given that csc #pi/4=sqrt2#, use an equivalent trigonometric expression to determine sec #3pi//4#?

1 Answer
Jim G.
Apr 24, 2018

#sec((3pi)/4)=-sqrt2#

Explanation:

#"using the "color(blue) "trigonometric identities"#

#•color(white)(x)csctheta=1/sintheta" and "sectheta=1/costheta"#

#•color(white)(x)sin(pi/2-theta)=costheta#

#•color(white)(x)cos(x+y)=cosxcosy-sinxsiny#

#csc(pi/4)=sqrt2rArrsin(pi/4)=1/sqrt2#

#rArrcos(pi/4)=sin(pi/4)=1/sqrt2#

#cos((3pi)/4)=cos(pi/4+pi/2)#

#color(white)(xxxxxx)=cos(pi/4)cos(pi/2)-sin(pi/4)sin(pi/2)#

#color(white)(xxxxxx)=1/sqrt2xx0-1/sqrt2xx1=-1/sqrt2#

#rArrsec((3pi)/4)=1/(-1/sqrt2)=-sqrt2#

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