Question

What is the value of \[\sin \pi \& \cos \pi \] ?

Answer 1

Hint: We know that the given functions are trigonometric functions. We have to find the value of those functions for the given angle. So we will use some identities and relations of these basic functions to get the value exactly.

Complete step-by-step answer:
Given that the functions are \[\sin \pi \& \cos \pi \]
We will check for each one by one.
 \[\sin \pi = \sin {180^ \circ }\]
Now we will use supplementary angle identity.
We know that, \[\sin \left( {{{180}^ \circ } - A} \right) = \sin A\]
Then we can write, \[\sin \left( {{{180}^ \circ } - {0^ \circ }} \right) = \sin {0^ \circ }\]
 We know that, \[\sin {0^ \circ } = 0\]
Thus we get, \[\sin {180^ \circ } = 0\]
That is nothing but in radians can be written as,
 \[\sin \pi = 0\]
This is the correct answer.

 \[\cos \pi = \cos {180^ \circ }\]
We can write this as \[\cos {180^ \circ } = \cos \left( {{{180}^ \circ } - {0^ \circ }} \right)\]
But we know the relation that, \[\cos \left( {{{180}^ \circ } - A} \right) = - \cos A\]
Thus we can say that, \[\cos \left( {{{180}^ \circ } - {0^ \circ }} \right) = - \cos {0^ \circ }\]
We know that \[\cos {0^ \circ } = 1\]
There is the last step,
 \[\cos {180^ \circ } = - \left( 1 \right)\]
And the answer is,
 \[\cos \pi = - 1\]
Thus simplified.

Note: Here note that if the same question appears in multiple choice then we should by heart the table for some particular values of angles. That will save time of ours. But in the theoretical case we need to elaborate the answer the way we did above.