Respuesta :
Hello from MrBillDoesMath!
Answer:
sqrt(15)/4
Discussion:
The attachment shows a right triangle where arcsin(@) = 1/4. (The arcsin means find the angle whose sine is 1/4 as is done in the triangle.) The missing side, sqrt(15), shown in red, was determined by the Pythagorean theorem.
Then cos(@) = cos(arcsin(1/4)) = sqrt(15)/4
Thank you,
MrB
The value of cos(arcsin( one fourth )) is 0.9682 to 4 decimal places.
cos(θ) = [tex]\frac{\sqrt{15} }{4}[/tex] ≈ 0.9682 to 4 decimal places
arcsin of some value gives you the angle that was used derive the that value of the sine.
sin, cos and tangent are just another way of defining ratios.
The value given can be used in conjunction with the properties of sine to determine a related triangle.
From this and using Pythagoras we can determine the length of the adjacent.
[tex]x^{2}+1^{2} =4^{2} \\x^{2} =16-1\\x=\sqrt{15}[/tex]
So, cos(θ) = [tex]\frac{\sqrt{15} }{4}[/tex] ≈ 0.9682 to 4 decimal places
Therefore, the value of cos(arcsin( one fourth )) is 0.9682 to 4 decimal places.
For more information:
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