Question

What is $ \tan (360^\circ - A) $ ?
A. $ \tan A $
B. $ - \tan A $
C. $ \cot A $
D. $ - \cot A $

Answer 1

Hint: Here we are given a tangent function with some angle and we need to find the equivalent tangent function, so here we will follow the All STC rule to find the equivalent trigonometric function.

Complete step by step solution:
The All STC rule, it is also known as ASTC rule in geometry. It states that all the trigonometric ratios in the first quadrant ( $ 0^\circ \;{\text{to 90}}^\circ $ ) are positive, sine and cosec are positive in the second quadrant ( $ 90^\circ {\text{ to 180}}^\circ $ ), tan and cot are positive in the third quadrant ( $ 180^\circ \;{\text{to 270}}^\circ $ ) and sin and cosec are positive in the fourth quadrant ( $ 270^\circ {\text{ to 360}}^\circ $ ).
By using the law of All STC rule, tangent is positive in the first and third quadrant and negative in the second and the fourth quadrant.
As, the given angle $ 360^\circ - A $ which lies in the fourth quadrant and tangent is negative in fourth quadrant and therefore $ \tan (360^\circ - A) = - \tan A $
Hence, from the given multiple choices, the option B is the correct answer.
So, the correct answer is “Option B”.

Note: Always remember the basic trigonometric identities for the accurate and an efficient solution. know the correlation between them as sine and cosec are inverse functions of each other, similarly tangent and cot are inverse of each other and secant and cosine are inverse of each other. Also, remember that the most important property of sines and cosines is that their values lie between minus one and plus one. Every point on the circle is unit circle from the origin. So, the coordinates of any point are within one of zero as well.
Directly the Pythagoras identity are followed by sines and cosines which concludes that – $ {\operatorname{Sin} ^2}\theta + {\operatorname{Cos} ^2}\theta = 1 $