In a right triangle ABC value of trigonometric function sin A = \(\frac{4\sqrt{41} }{41}\) (with rational denominator).
What is trigonometric function?
" Trigonometric function are defined as the relation between the acute angle of a right angled triangle to the ratio of the sides of the triangle."
Formula used
In a right angled triangle,
Sinθ = (Opposite side )/ Hypotenuse
'θ' one of the acute angle of the right angled triangle
Pythagoras theorem
In ΔACB
(Hypotenuse)² = (Opposite side)² + ( Adjacent side)²
c² = a² +b²
According to the question,
As shown in the diagram,
In right angled triangle ACB,
Given ,
∠C = 90°
Opposite side 'a' = 4
Adjacent side 'b' = 5
Substitute the value in formula to calculate hypotenuse we get,
(c)² = (4)² +(5)²
⇒c² = 16 +25
⇒ c = √41
Substitute the value in trigonometric function we get,
sin A = 4 / √41
\(= \frac{4}{\sqrt{41}} *\frac{\sqrt{41} }{\sqrt{41} } \\\\=\frac{4\sqrt{41} }{41}\)(rational denominator)
Hence, value of trigonometric function sin A = \(\frac{4\sqrt{41} }{41}\) (with rational denominator).
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