Question #c6847

1 Answer
Jim G.
Aug 20, 2017

#"see explanation"#

Explanation:

#"given "csctheta=3" then"#

#•color(white)(x)sintheta=1/csctheta=1/3#

#"since "sintheta>0" this indicates that "theta# is in the first or second quadrant.

#•color(white)(x)costheta=+-sqrt(1-sin^2theta)#

#color(white)(xxxxxx)=-sqrt(1-1/9)=-sqrt(8/9)#

#color(white)(xxxxxx)=-(2sqrt2)/3#

#•color(white)(x)sectheta=1/costheta=-1/((2sqrt2)/3)=-3/(2sqrt2)=-(3sqrt2)/4#

#•color(white)(x)tantheta=sintheta/costheta=(1/3)/(-(2sqrt2)/3)=-1/(2sqrt2)=-sqrt2/4#

#•color(white)(x)cottheta=1/tantheta=1/(-sqrt2/4)=-4/sqrt2=-2sqrt2#

#theta" is in the second quadrant"#

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