Question

Find the sign of $$\sin 300$$?

Answer 1

Hint: We are given above to find the sign of $$\sin 300$$. We will try to find it by using the graphical properties of trigonometric functions. We should know the signs of sin function on various quadrants in a Cartesian plane. A Cartesian plane is divided into four quadrants of $${90}^{\circ }$$ each. First we locate the position of $$\sin 300$$ in the given quadrant and then use graphical properties of trigonometric functions to find the sign of $$\sin 300$$.

Complete step-by-step solution:
First of all we have to locate $$\sin 300$$ in a quadrant using the graphical properties of trigonometric functions. First quadrant is between $$0^{\circ }$$to $${90}^{\circ }$$, second quadrant is between $${90}^{\circ }$$ to $${180}^{\circ }$$, third quadrant is between $${180}^{\circ }$$ to $${270}^{\circ }$$ and fourth quadrant is between $${270}^{\circ }$$ to $${360}^{\circ }$$.
Sign of sin function in the first quadrant is positive, in the second quadrant is positive, in third quadrant is negative and fourth quadrant is negative, as given below
First quadrant $${}^{\prime }{+}^{\prime }$$
Second quadrant $${}^{\prime }{+}^{\prime }$$
Third quadrant $${}^{\prime }{-}^{\prime }$$
Fourth quadrant $${}^{\prime }{-}^{\prime }$$
Since we are dealing with$${300}^{\circ }$$, it is located in the fourth quadrant. Hence the sign of $$\sin 300$$ will be $${}^{\prime }{-}^{\prime }$$.

Note: This is to note that we have to remember signs for all the trigonometric functions in different quadrants. We also have to remember the conversion of different trigonometric functions into each other. For example, for $$\sin 300$$, we know the sign is negative but we do not know its value. So we convert it into an angle whose trigonometric value can be found easily. For this we know that $$\sin (360-\theta )=-\sin \theta$$. So $$\sin 300$$ can be written as $$\sin (360-300)=-\sin 60$$, whose value we know is $$-{\displaystyle \frac{\sqrt{3}}{2}}$$.