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

Hint: In the given question, we have been asked to calculate the exact value of a trigonometric ratio in sine. The argument (or here, we can say the angle) of the ratio is also given. We just need to calculate the answer of the ratio. The trick here is the sign of the answer. We need to see if the negative of the angle of sine changes the value of the ratio too or does it remain the same like in cosine’s case.

Complete step-by-step answer:
We have to calculate the value of \[\sin \left( { - 90} \right)\]. For calculating that, we ignore the negative sign with the angle, calculate the answer and then just attach the ignored negative sign with the answer.
Now, \[\sin 90^\circ = 1\]
So, \[\sin \left( { - 90} \right) = - \sin \left( {90} \right) = - 1\]

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. So, when there is a negative sign inside the trigonometric ratio in sine, we calculate the value by ignoring the negative sign, write the answer and then just attach the ignored negative sign with the answer.