To determine the value of [tex]\(\cos 90^{\circ}\)[/tex], we can use the trigonometric identities and the unit circle.
1. Trigonometric Identity:
In trigonometry, we know that:
[tex]\[
\sin^2(\theta) + \cos^2(\theta) = 1
\][/tex]
Given that [tex]\(\sin 90^{\circ} = 1\)[/tex], we can substitute this value into the identity:
[tex]\[
1^2 + \cos^2(90^{\circ}) = 1
\][/tex]
This simplifies to:
[tex]\[
1 + \cos^2(90^{\circ}) = 1
\][/tex]
2. Solving for [tex]\(\cos 90^{\circ}\)[/tex]:
[tex]\[
\cos^2(90^{\circ}) = 1 - 1
\][/tex]
[tex]\[
\cos^2(90^{\circ}) = 0
\][/tex]
Taking the square root of both sides:
[tex]\[
\cos(90^{\circ}) = 0
\][/tex]
Therefore, the value of [tex]\(\cos 90^{\circ}\)[/tex] is [tex]\(0\)[/tex].
So, in the given options, the correct answer is:
[tex]\[ 0 \][/tex]
