What is the exact value of sin when cos x =1/√10?

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SUMMARY

The exact value of sin when cos x = 1/√10 can be determined using the Pythagorean identity sin²x + cos²x = 1. Given that cos x = 1/√10, we find sin²x = 1 - (1/√10)², which simplifies to sin²x = 1 - 1/10 = 9/10. Therefore, sin x = √(9/10) = 3/√10. Since x is in the first quadrant, sin x is positive, resulting in sin x = 3/√10.

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ohhnana
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Homework Statement



cos x is a first quadrant angle in standard position and cos x =1/√10 . Find the exact value of sin .

Homework Equations



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The Attempt at a Solution


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Hint: Remember the definition of sine and cosine.
 
I would suggest drawing a triangle with the fraction result of cos x distributed on the appropriate edges. You should be able to 'fill in the blanks'
 
ohhnana said:

Homework Statement



cos x is a first quadrant angle in standard position and cos x =1/√10 . Find the exact value of sin .

Homework Equations



?

The Attempt at a Solution


?
Excerpt from the forum rules (https://www.physicsforums.com/showthread.php?t=414380)
Homework Help:
You MUST show that you have attempted to answer your question in order to receive help. You MUST make use of the homework template, which automatically appears when a new topic is created in the homework help forums.
 

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