Question

find the indicated function value. if it is undefined, say so.
sin (-90°)

select the correct choice below and, if necessary, fill in the answer box to complete your choice.

a. sin (-90°)=
(simplify your answer, including any radicals. use integers or fractions for any numbers in the expression.)

b. the function is undefined.

Explanation:

Step1: Use the odd - function property of sine

The sine function is an odd function, which means that \(\sin(-\theta)=-\sin(\theta)\) for any angle \(\theta\). So, for \(\sin(- 90^{\circ})\), we can rewrite it as \(-\sin(90^{\circ})\).

Step2: Recall the value of \(\sin(90^{\circ})\)

We know from the unit - circle or basic trigonometric values that \(\sin(90^{\circ}) = 1\).

Step3: Calculate \(\sin(-90^{\circ})\)

Substitute \(\sin(90^{\circ}) = 1\) into \(-\sin(90^{\circ})\), we get \(\sin(-90^{\circ})=-1\).

Answer:

A. \(\sin(-90^{\circ})=\boxed{-1}\)