Question

How do you find the exact value of $\sin {30^ \circ } - \sin {60^ \circ }$?

Answer 1

Hint: We can solve this question by applying the trigonometric values assigned of each angle, where ${30^ \circ }$ and ${60^ \circ }$ are angles. In the second quadrant only sine and its reciprocal cosecant remains positive and along with the first quadrant where all the wanted sine, cosine, tangent remains positive. Also remember the trigonometry table so that we can quickly assign the values as per the angles. For example, has the value assigned as -1 in the trigonometric table. Also is equal to zero.

Complete Step by step answer:
In order to solve this question, we must know the trigonometry table.
In order to solve this question, we will assign the value of $\sin {30^ \circ } = \dfrac{1}{2}$and $\sin {60^ \circ } = \dfrac{{\sqrt 3 }}{2}$
Substituting in the original question the values of trigonometry assigned to each angle.
On applying we get,
= $\sin {30^ \circ } - \sin {60^ \circ }$
= $\dfrac{1}{2} - \dfrac{{\sqrt 3 }}{2}$.
And so as per the standard values the values are substituted and if we simplify further we have,
= $\dfrac{{1 - \sqrt 3 }}{2}$.

Note : The exact value of sin 30 degrees is 0.5 can be also expressed as, $\sin {30^ \circ } = \dfrac{1}{2}$. The exact value of sin 60 degrees is 0.8 can be also expressed as, $\sin {60^ \circ } = \dfrac{{\sqrt 3 }}{2}$. The sine function can be expressed as angle which is equal to the length of opposite side divided by the length of hypotenuse side and the formula is given, \[sin\theta = \dfrac{{opposite\;side}}{{hypotenuse\;side}}\]
Learn the standard values of trigonometry angles by heart.