Question

Evaluate the following: $\sin 30^\circ - \cos 30^\circ $ .

Answer 1

Hint: We can see that in the above we have been a trigonometric expression. We will try to remember the values of the given trigonometric ratios for the given corresponding angles and then we substitute the values in the equation. After that we will simplify the equation to get the answer.

Complete step by step answer:
Here we have $\sin 30^\circ - \cos 30^\circ $ .
We should know the values of the following trigonometric ratios:

$\theta $	$0^\circ $	$30^\circ $	$45^\circ $	$60^\circ $	$90^\circ $
$\sin $	$0$	$\dfrac{1}{2}$	$\dfrac{1}{{\sqrt 2 }}$	$\dfrac{{\sqrt 3 }}{2}$	$1$
$\cos $	$1$	$\dfrac{{\sqrt 3 }}{2}$	$\dfrac{1}{{\sqrt 2 }}$	$\dfrac{1}{2}$	$0$

From the above table we get that the value of
$\sin 30^\circ = \dfrac{1}{2}$
And the value of
$\cos 30^\circ = \dfrac{{\sqrt 3 }}{2}$
Now we will substitute the values in the given equation:
$\dfrac{1}{2} - \dfrac{{\sqrt 3 }}{2}$
On simplifying we have
$\dfrac{{1 - \sqrt 3 }}{2}$
Hence the required value is $\dfrac{1}{2}\left( {1 - \sqrt 3 } \right)$ .

Note:
We should always remember the values of all other trigonometric ratios with their corresponding angles too. The values of the angles that lie in the first quadrant are positive for all.
ratios, while in the second quadrant the value of sine and cosec is positive.
Similarly in the third quadrant, the value of tangent $(\tan )$ and cotangent $(\cot )$ is positive. And in the fourth quadrant the value of cosine $(\cos )$ and secant i.e. $(\sec )$ is positive.