Find csc theta and cot theta if tan theta=-4/3 and sin theta > 0?
1 Answer
Feb 7, 2018
Explanation:
#"using the "color(blue)"trigonometric identities"#
#•color(white)(x)cottheta=1/tantheta#
#•color(white)(x)csc^2theta=1+cot^2theta#
#"here "tantheta=-4/3#
#rArrcottheta=1/(-4/3)=-3/4#
#rArrcsc^2theta=1+(-3/4)^2#
#color(white)(xxxxxx)=1+9/16=25/16#
#"since "tantheta<0" and "sintheta>0#
#"then "theta" is in the second quadrant"#
#rArrcsctheta=sqrt(25/16)=5/4#
