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the value of sin ∅ is 12/ 13
<h3>Quadrants and the "cast" Rule:</h3>- In the first quadrant, the values for sin, cos, and tan are positive.
- In the second quadrant, the values for sin are positive only.
- In the third quadrant, the values for tan are positive only.
- In the fourth quadrant, the values for cos are positive only.
From the given question,
We have, cos ∅= 5/13
From the trigonometric identities, we have that
Then , let's substitute the value of cos ∅
Let make sin the subject of formula and find the squares of the fraction
sin²∅ =
Find the LCM
sin²∅ =
Find the difference
sin²∅ =
Find the square root
sin∅ =
sin∅ =
In quadrant II , sin is positive, so we have
sin ∅ = 12/ 13
Thus, the value of sin ∅ is 12/ 13
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