# Evaluate the following trigonometric term

$\sin {30^0}\cos {30^0}$

Last updated date: 23rd Mar 2023

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Answer

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Hint- Use the values of the following terms from the trigonometric table and find the product directly. These are one of the most important values to be remembered.

“Complete step-by-step answer:”

Given term: $\sin {30^0}\cos {30^0}$

As we know from the trigonometric table that

\[

\sin {30^0} = \dfrac{1}{2} \\

\cos {30^0} = \dfrac{{\sqrt 3 }}{2} \\

\]

So in order to find the value of the given term. We multiply both the terms

\[

\Rightarrow \sin {30^0}\cos {30^0} = \dfrac{1}{2} \times \dfrac{{\sqrt 3 }}{2} \\

= \dfrac{{\sqrt 3 }}{4} \\

= \dfrac{{1.732}}{4}\left[ {\because \sqrt 3 = 1.732} \right] \\

= 0.433 \\

\]

Hence, the value of $\sin {30^0}\cos {30^0}$ is \[\dfrac{{\sqrt 3 }}{4}{\text{ or }}0.433\]

Note- We know that sine of any angle in a right angled triangle is the ratio of the lengths of height upon the hypotenuse and cosine of any angle in a right angled triangle is the ratio of the lengths of base upon hypotenuse. The value of sine and cosine of some common angles like ${0^0},{30^0},{45^0},{60^0},{90^0},{180^0}$ are very important and they must be remembered.

“Complete step-by-step answer:”

Given term: $\sin {30^0}\cos {30^0}$

As we know from the trigonometric table that

\[

\sin {30^0} = \dfrac{1}{2} \\

\cos {30^0} = \dfrac{{\sqrt 3 }}{2} \\

\]

So in order to find the value of the given term. We multiply both the terms

\[

\Rightarrow \sin {30^0}\cos {30^0} = \dfrac{1}{2} \times \dfrac{{\sqrt 3 }}{2} \\

= \dfrac{{\sqrt 3 }}{4} \\

= \dfrac{{1.732}}{4}\left[ {\because \sqrt 3 = 1.732} \right] \\

= 0.433 \\

\]

Hence, the value of $\sin {30^0}\cos {30^0}$ is \[\dfrac{{\sqrt 3 }}{4}{\text{ or }}0.433\]

Note- We know that sine of any angle in a right angled triangle is the ratio of the lengths of height upon the hypotenuse and cosine of any angle in a right angled triangle is the ratio of the lengths of base upon hypotenuse. The value of sine and cosine of some common angles like ${0^0},{30^0},{45^0},{60^0},{90^0},{180^0}$ are very important and they must be remembered.

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