Step-by-step explanation:
In Quadrant II, cosine is negative.
We know that sin²x + cos²x = 1, so:
cosx = sqrt[1 - sin²x]
= sqrt[1 - (5/13)²]
= sqrt(144/169)
= -12/13 (since cosx is negative here)
The answer is -12/13. (B)
Option B is correct.
According to the given question
We have, sin ∅ = 5/13
From the trigonometric identities we know that
[tex]sin^{2}[/tex]∅ + [tex]cos^{2}[/tex]∅ =1
substitute the value of sin∅ in the above identity
[tex](\frac{5}{13} )^{2} + cos^{2}[/tex]∅ =1
⇒ [tex]\frac{25}{69} +cos^{2}[/tex]∅ =1
⇒ [tex]cos^{2}[/tex]∅ = 1 - [tex]\frac{25}{169}[/tex]
⇒ [tex]cos^{2}[/tex]∅ = [tex]\frac{169-25}{69} =\frac{144}{169}[/tex]
⇒[tex]cos[/tex]∅ = [tex]\sqrt{\frac{144}{169} }[/tex]
⇒cos∅ = ±[tex]\frac{12}{13}[/tex]
Since, ∅ is in quadrant II, then cos<0
⇒ cos∅ = -[tex]\frac{12}{13}[/tex]
Hence, option B is correct.
Learn more about quadrant and cast rule here:
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