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If tan theta= -3/4 and θ is in quadrant IV, cos2 theta= and tan2 theta= .

User Jim Jam
by
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1 Answer

5 votes


\cos 2(\text { theta })=(7)/(25)


\tan 2(\text { theta })=-(24)/(7)

Explanation:

Given data:


\tan \theta=-(3)/(4)

To find:

cos 2 theta and tan 2 theta

Solution:

Hence, the trigonometric formula for those are below,


\tan 2(\text { theta })=\frac{2 \tan (\text { theta })}{1-\tan ^(2)(\text { theta })}


\cos 2(\text { theta })=\frac{1-\tan ^(2)(\text { theta })}{1+\tan ^(2)(\text { thet } a)}

Now, find the required data by substituting the given value. We get,


\tan 2(\text { theta })=(2 *\left(-(3)/(4)\right))/(1-(9)/(16))=-(3)/(2) * (16)/(7)=-(24)/(7)

Similarly for cos 2 theta,


\cos 2(\text { theta })=(1-(9)/(16))/(1+(9)/(16))=(7)/(16) * (16)/(25)=(7)/(25)

User Alex Coppock
by
7.3k points
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