How do you find the value for $sin2theta$ , $cos2theta$ , and $tan2theta$ and the quadrant in which $2theta$ lies given $sintheta=4/5$ and $theta$ is in quadrant I?

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Answer 1 · 2016-10-01T16:17:41

$sin2theta=24/25$ , $cos2theta=-7/25$ and $tan2theta=-24/7$

As $sintheta=4/5$ and it is first quadrant, all trigonometric ratios of $theta$ are positive.

and $costheta=sqrt(1-(4/5)^2)$

= $sqrt(1-16/25)=sqrt(9/25)=3/5$

and $tantheta=(4/5)/(3/5)=4/5xx5/3=4/3$

Now $sin2theta=2sinthetacostheta=2xx4/5xx3/5=24/25$

$cos2theta=2cos^2theta-1=2xx(3/5)^2-1$

= $2xx9/25-1=18/25-1=-7/25$

$tan2theta=(24/25)/(-7/25)=24/25xx25/(-7)=-24/7$

How do you find the value for sin2thetasin2theta, cos2thetacos2theta, and tan2thetatan2theta and the quadrant in which 2theta2theta lies given sintheta=4/5sintheta=4/5 and thetatheta is in quadrant I?