Respuesta :
Trigonometric function gives the ratio of different sides of a right-angle triangle. The value of Cos(x), if the value of Sin(x) is 0.3 is 0.954.
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.
As the value of sin(x) is given to us, therefore, we will find the value of x firstly,
[tex]\rm Sin(x)=0.3\\\\x = Sin^{-1}\ 0.3\\\\x = 17.4576[/tex]
Therefore, the value of cos(x) can be written as,
[tex]\rm Cos(x)\\\\= Cos(17.4576)\\\\= 0.9539\approx 0.954[/tex]
We can also use the trigonometric property, therefore,
[tex]\rm (Sin\ x)^2 +(Cos\ x)^2=1\\\\0.3^2 + (Cos\ x)^2 = 1\\\\Cos(x) = \sqrt{1-0.3^2}\\\\Cos(x)=0.954[/tex]
Hence, the value of Cos(x), if the value of Sin(x) is 0.3 is 0.954.
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