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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]

Select the best answer from the choices provided.

Sagot :

GinnyAnswer
Let's solve the problem step by step.

We are given that:

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

We are asked to find [tex]\(\sin(90^\circ - x)\)[/tex].

To do this, we can use a fundamental trigonometric identity, specifically the co-function identity, which states:

[tex]\[ \sin(90^\circ - x) = \cos(x) \][/tex]

Given this identity, we substitute the given value of [tex]\(\cos(x)\)[/tex]:

[tex]\[ \sin(90^\circ - x) = \frac{1}{3} \][/tex]

Thus, the correct answer is:

[tex]\[ \boxed{\frac{1}{3}} \][/tex]
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