Respuesta :
Answer:
8 / √89
Step-by-step explanation:
1. cot (x) = 5/8
2. 8√89 / 89
3. simplify
4. 8 / √89
Value of sin(x) is equals to (8√89) / (89), 0 < x < 90.
What are trigonometric functions?
" Trigonometric functions are mathematical functions which relates angles and sides of a right angle triangle , where 0 < x < 90°."
Formula used
In right angled triangle ABC , ∠B = 90° , ∠C = x°
cot (x )= ( Base ) / ( Opposite side)
sin ( x) = ( Opposite side ) / ( Base )
Pythagoras theorem
(Hypotenuse)² = (Base)² + (Opposite side)²
(AC)² = (AB)² + (BC)²
According to the question,
Given
cot (x) =5 / 8 , 0< x< 90
Therefore, by comparing the given values of trigonometric function with the formula we have,
Base = 5
Opposite side = 8
Substitute the value in the Pythagoras theorem we get,
(Hypotenuse)² = 5² + 8²
⇒ (Hypotenuse)² = 25 + 64
⇒ Hypotenuse = √89
Therefore,
sin(x) = 8 / √89
= 8√89 / 89 ( rationalize √89)
Hence, value of sin(x) is equals to (8√89) / (89), 0 < x < 90.
Learn more about trigonometric function here
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