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Determine the amplitude of y equals -2 sin x?
The amplitude of the wave [ y = -2 sin(x) ] is 2.
How do you prove that 2 sin 3x divided by sin x plus 2 cos 3x divided by cos x equals 8 cos 2x?
You need to know the trigonometric formulae for sin and cos of compound angles. sin(x+y) = sin(x)*cos(y)+cos(x)*sin(y) and cos(x+y) = cos(x)*cos(y) - sin(x)*sin(y) Using these, y = x implies that sin(2x) = sin(x+x) = 2*sin(x)cos(x) and cos(2x) = cos(x+x) = cos^2(x) - sin^2(x) Next, the triple angle formulae are: sin(3x) = sin(2x + x) = 3*sin(x) - 4*sin^3(x) and cos(3x) = 4*cos^3(x) - 3*cos(x) Then the left hand side = 2*[3*sin(x) - 4*sin^3(x)]/sin(x) + 2*[4*cos^3(x) - 3*cos(x)]/cos(x) = 6 - 8*sin^2(x) + 8cos^2(x) - 6 = 8*[cos^2(x) - sin^2(x)] = 8*cos(2x) = right hand side.
Name any lines of symmetry for the graph of y equals sin x?
x = (2n+1)*pi/2 radians for any integer n.
What is the period of tan x?
The period of the function y= tan(x) is pie The periods of the functions y= cos(x) and y= sin(x) is 2pie
What is the transformation that maps y equals sinx onto y equals the inverse of sinx?
f(x) = 1/x except where x = 0.
