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Given that [tex]\cos (x)=\frac{1}{3}[/tex], find [tex]\sin (90^\circ - x)[/tex].

A. [tex]-\frac{2}{3}[/tex]
B. [tex]-\frac{1}{3}[/tex]
C. [tex]\frac{1}{3}[/tex]
D. [tex]\frac{2}{3}[/tex]

Please select the best answer from the choices provided.

Sagot :

GinnyAnswer
Sure, let's solve the problem step-by-step:

Given: [tex]\(\cos (x) = \frac{1}{3}\)[/tex]

We need to find: [tex]\(\sin (90^\circ - x)\)[/tex]

First, recall the co-function identity for sine and cosine:
[tex]\[ \sin(90^\circ - x) = \cos(x) \][/tex]

Using this identity:
[tex]\[ \sin(90^\circ - x) = \cos(x) \][/tex]

We are given that:
[tex]\[ \cos(x) = \frac{1}{3} \][/tex]

So, we can substitute this value to get:
[tex]\[ \sin(90^\circ - x) = \frac{1}{3} \][/tex]

Thus, the value of [tex]\(\sin (90^\circ - x)\)[/tex] is [tex]\(\frac{1}{3}\)[/tex].

Therefore, the correct answer is:
[tex]\[ C. \frac{1}{3} \][/tex]
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