Question

 Find the value of \[\tan \left( { - 945} \right)^\circ \].
A. \[ - 1\]
B. \[ - 2\]
C. \[ - 3\]
D. \[ - 4\]

Answer 1

Hint:
Here the angle is negative and \[\tan \left( { - \theta } \right) = - \tan \theta \]. Express the angle \[945^\circ \] as \[\left( {(2a+1) \times 180^\circ \pm b} \right)\]. To find the values of \[a\] and \[b\], divide \[945\] by \[180\]. If the value of \[a\] is odd, then change the trigonometric ratio and if it is even then the ratio will be the same. Thus the angle is transformed into a standard angle of which the value is known. Putting the value you will get the required answer.



Formula Used:
Negative angle of tangent:
\[\tan \left( { - \theta } \right) = - \tan \theta \]


Complete step-by-step answer:
Here \[\theta = 945^\circ \]
So, \[\tan \left( { - 945} \right)^\circ = - \tan 945^\circ \]
Simplify the angle
\[- \tan 945^\circ \] = \[- \tan \left( {5 \times 180^\circ + 45^\circ } \right)\]
We know that, \[ \tan [(2n+1) \pi + \theta] \] = \[ \tan \theta \]
Here \[180\] is multiplied by \[5\], so the ratio will not be changed and the expression will reduce to \[\tan 45^\circ \]
And value of \[\tan 45^\circ \] is \[1\].
So, \[- \tan \left( { 945} \right)^\circ = - \tan 45^\circ = - 1\]
Hence, option A is correct.


Additional information:
There are four quadrants of a coordinate system. In the first quadrant, all ratios of trigonometry are positive. In the second quadrant, sine and cosec are positive. In the third quadrant, tangent and cotangent are positive. In the fourth quadrant, cosine and secant are positive.




Note:
First of all, you should look at the sign of the angle. Positive angles are formed by rotating a line counterclockwise and negative angles are formed by rotating clockwise. Here the angle is negative. So, make the angle positive at first.