Question

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

Answer 1

`\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)`