The trigonometric function gives the ratio of different sides of a right-angle triangle. The value of Cosec A is (√61)/(6).
What are Trigonometric functions?
The trigonometric function gives the ratio of different sides of a right-angle triangle.
[tex]\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Tan \theta=\dfrac{Perpendicular}{Base}\\\\\\Cosec \theta=\dfrac{Hypotenuse}{Perpendicular}\\\\\\Sec \theta=\dfrac{Hypotenuse}{Base}\\\\\\Cot \theta=\dfrac{Base}{Perpendicular}\\\\\\[/tex]
where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite to the 90° angle.
The Cot is the ratio of the base of the triangle to the perpendicular side of the triangle, therefore, we can write,
Cot A = Base/Perpendicular = 5/6
Thus, the base of the triangle is 5 units, while the length of the perpendicular of the triangle is 6 units. Now the length of the hypotenuse side of the triangle is,
H² = 5² + 6²
H² = 25 + 36
H = √61
Now, the value of Cosec A can be written as,
Cosec A = Hypotenuse/Perpendicular = (√61) / (6)
Hence, the value of Cosec A is (√61)/(6).
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