What is the value of sin theta if cos theta = -2/11 and is in the second quadrant?

im stuck on what im supposed to do!

1 Answer
Jim G.
May 19, 2018

#sintheta=3/11sqrt13#

Explanation:

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

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

#rArrsintheta=+-sqrt(1-cos^2theta)#

#"since "costheta<0" and in second quadrant"#

#"then "sintheta>0#

#rArrsintheta=+sqrt(1-(-2/11)^2)#

#color(white)(rArrsintheta)=sqrt(1-4/121)#

#color(white)(rArrsintheta)=sqrt(117/121)#

#color(white)(rArrsintheta)=sqrt117/11=(3sqrt13)/11#

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