I have the negatives, you can find the positive

Rule of 360 degrees:

Firstly, $\sin { x° }$ is positive if $0°<x\quad\left( mod\quad 360 \right) <180°$ . As $1290°\quad\left( mod\quad 360 \right)=210°$ , $\sin { 1290° }$ is negative.

Secondly, $\cot { x° }$ is positive if $\tan { x° }$ is positive, and this is positive if $0°<x\quad\left( mod\quad 180 \right) <90°$ , which is not the case here as $1200°\quad\left( mod\quad 180 \right)=120°$ .

Thirdly, $\cos { x° }$ is positive in the ranges $0°<x\quad\left( mod\quad 360 \right) \le 90°$ and $270°<x\quad\left( mod\quad 360 \right) \le 360°$ , but $570°\quad\left( mod\quad 360 \right)=210°$ and is therefore negative.

This leaves us with $\large \color{#20A900}{\boxed{\tan { 960° }}}$ as the answer, but for the record, $960°\quad\left( mod\quad 180 \right)=60°$ and is therefore positive.

We know that sin is positive in I and II quadrants, cos in I and IV quadrants and tan (and hence cot) in I and III quadrants. Also, we can 'reduce' the angles greater than 360 deg to fall within the principal range (0 to 360 deg) by dividing the given measure by 360 and taking its remainder as the new angle. In the choices given with the question, only tan 960 deg is positive because 960/360=(2*360)+240 which means that tan 960=tan 240 and as we know that 240 deg falls in the III quadrant, the tan function of any such angle is also positive.

Take out 360 as many as possible and then see the remaining number and use the following parameter,

1. If the angle lies in 1st Quadrant i.e.; 0 to 90 All trigonometric functions are positive,
2. If the angle lies in 2nd Quadrant i.e; 91 to 180 Only Sin Function is positive and rest are negative
3. If it lies in 3rd i.e.; 181 to 270 Only Tangent Function is positive (of-course Cotangent will also be +ve)
4. If angle lies in 4th quadrant i.e.; 271 to 359; Only Cosine functions are positive,

So in case 1 that is 1290, Take out as many 360 as possible and the remaining digit that is left is 210 that lies in 3rd quadrant where only Tangent is positive so it will be negative,

In case 2 the left over digit is 240 that again is in 3rd Quadrant where Tangent is the only positive function so it'll be positive and hence you reached the anwser in 2nd option

Convert all to 0<x<360. tan960 = tan 240 (+ve)

All functions are positive in the first quadrant; Only Sin functions are positive in the second quadrant; Tan functions are positive in the third quadrant and Cos functions are positive in the fourth quadrant... 960 will lie in the third quadrant where only tan is positive...

All Students Take Calculus! All, Sine, Tangent, Cosine - Which function(s) is/are positive in all four quadrants, including their reciprocals.

tan 960 = tan 240 which is between 180 and 270 and thus positive.