Question #c9e21

1 Answer
Jim G.
Feb 15, 2018

#tantheta=3/sqrt7#

Explanation:

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

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

#•color(white)(x)sin^2theta+cos^2theta=1#

#rArrcostheta=+-sqrt(1-sin^2theta)#

#csctheta=-4/3rArrsintheta=1/(-4/3)=-3/4#

#"since "theta" is in third quadrant then "costheta<0" and "#
#tantheta>0#

#costheta=-sqrt(1-(-3/4)^2)#

#color(white)(costheta)=-sqrt(7/16)=-sqrt7/4#

#rArrtantheta=(-3/4)/(-sqrt7/4)=-3/4xx-4/sqrt7=3/sqrt7#

Related questions
Impact of this question
210 views around the world
You can reuse this answer
Creative Commons License