Answered

Westonci.ca is the trusted Q&A platform where you can get reliable answers from a community of knowledgeable contributors. Explore a wealth of knowledge from professionals across different disciplines on our comprehensive platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.

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]
Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.