Question

How do you find the value of \[\cos \left( { - 90} \right)\]?

Answer 1

Hint:
In the given question, we have been asked to calculate the value of a trigonometric ratio. The argument of the trigonometric ratio has also been given. When the denominator of the value of the trigonometric is an irrational number, we shift the irrational part to the numerator by rationalizing the denominator. And then we solve the answer as normal.

Formula Used:
We are going to use the formula that the negative of an angle in cosine is same as the positive angle,
\[\cos \left( { - x} \right) = \cos \left( x \right)\]

Complete step by step answer:
We have to calculate the value of \[\cos \left( { - 90} \right)\].
Now, we know that \[\cos \left( { - x} \right) = \cos x\]
Hence, \[\cos \left( { - 90} \right) = \cos \left( {90} \right)\]
And, \[\cos \left( {90} \right) = 0\]

Hence, \[\cos \left( { - 90} \right) = 0\]

Additional Information:
In this question, we were given cosine with a negative angle. We converted it to positive by doing nothing, just removing the sign because \[\cos \left( { - x} \right) = \cos \left( x \right)\].
But, if it were the sine then we had to bring the negative sign out, hence,
\[\sin \left( { - x} \right) = - \sin x\]

Note:
So, for solving questions of such type, we first write what has been given to us. Then we write down what we have to find. Then we write the formula which connects the two things. We saw that in this question, we did not need to do any effort to rationalize the denominator – the effort is needed only when a denominator is an irrational number.