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Show that 6sin(60◦) + 5tan(60◦) can be written in the form √k where k is an integer.

sin(60◦) = √3 /2 tan(60◦) = √3 6sin(60◦) + 5tan(60◦) = 3√3 + 5√3 = 8√3 = √64√3 = √192
AG
Answered by Alistair G. • Maths tutor
4397 Views

Find all solutions to the equation 8sin^2(theta) - 4 = 0 in the interval 2(pi) < (theta) < 4(pi)

First substiute sin(theta) = x (This step is not nesecessary but often people find quadratics easier to solve in variables that they usually use). Then due to the fact that the &quot;b&quot; coefficient in t...
NB
Answered by Nicholas B. • Maths tutor
6995 Views

How can I find the derivative of y = tan(x)?

Let's first recall the definition of tan(x) = sin(x)/cos(x). Hence, y' = d/dx( sin(x)/cos(x) ). Recall quotient rule for differentiation: ( f(x)/g(x) )' = ( f '(x)^2*g(x) - f(x)*g'(x)^2 ) / g(x)^2 and that d...
RB
Answered by Riccardo B. • Maths tutor
6109 Views

Solve the following equations x^2-2x+4=0, x^2+4x+1=0

x 2 -2x+4= (x-2)(x-2)=0 x=-2 (double root) x 2 +5x+1=0 x 1,2 = -5+_ (5 2 -4(1)(1) ) 0.5 /2 x 1 =4.8 x 2 =-0.2 (to 1 d.p.)
KF
Answered by Kyriakos F. • Maths tutor
3703 Views

y = 4x / (x^2 + 5). Find dy/dx.

We use the quotient rule here which states that if y = f(x)/g(x) then dy/dx = (f'(x)g(x) - g'(x)f(x)) / (g(x)^2). Here f(x) = 4x and g(x) = x^2 + 5, so we have f'(x) = 4 , g'(x) = 2x. This gives us dy/dx = (...
PS
Answered by Patrick S. • Maths tutor
11196 Views