Question

What are the six trigonometric values of $\dfrac{\pi}{6}$?

Answer 1

Hint: We mainly know six trigonometric functions that are sin, cos, tan, cosec, sec, cot which we are familiar with. We know that sin and cos function values lie between 1 and -1 and similarly every other trigonometric function has their own domain and range.

Complete step-by-step answer:
The value of sin function at $\dfrac{\pi}{6}$ is given by $\sin \dfrac{\pi }{6}=\dfrac{1}{2}$
Similarly, value of cos at $\dfrac{\pi}{6}$ is given by $\cos \dfrac{\pi }{6}=\dfrac{\sqrt{3}}{2}$
Similarly, value of tan at $\dfrac{\pi}{6}$ is given by $\tan \dfrac{\pi }{6}=\dfrac{1}{\sqrt{3}}$
Similarly, value of cot at $\dfrac{\pi}{6}$ is given by $\cot \dfrac{\pi }{6}=\sqrt{3}$ also this value can be attained by reciprocal of the value attained in tangent function.
Similarly, value of sec at $\dfrac{\pi}{6}$ is given by $\sec \dfrac{\pi }{6}=\dfrac{2}{\sqrt{3}}$also this value can be attained by reciprocal of the value attained in cosine function.
Similarly, value of cosec at $\dfrac{\pi}{6}$ is given by $\cos ec\dfrac{\pi }{6}=2$ also this value can be attained by reciprocal of the value attained in sine. function.
Hence we got the various trigonometric ratios.

Note: We must take the sides that are marked base and hypotenuse correctly so that we get the correct ratios and should remember that the side along which we mention the angle theta is always the base. We can also verify all these value by making a right-angled triangle and then taking angle as $\dfrac{\pi}{6}$, we will get the same answer.