Question #59458

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Answer 1 · 2017-12-06T15:56:19

#sintheta=0.8958# ( 4 .d.p.)

Identity:

#color(red)(sin^2theta+cos^2theta=1)#

#cos^2x=1-sin^2x#

#:.#

#cos^2theta=(-4/9)^2=16/81#

Hence:

#1-sin^2theta=16/81#

#sin^2theta= 1-16/81=65/81#

#sintheta=sqrt(65/81)=+-sqrt(65)/9=+-0.8958064164#

The sine is positive in quadrant II, so:

#sintheta=0.8958# ( 4 .d.p.)