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The function f(x) is defined by f(x) = 1 + 2 sin (3x), − π/ 6 ≤ x ≤ π/ 6 . You are given that this function has an inverse, f^ −1 (x). Find f^ −1 (x) and its domain

To find inverse functions we swap the variables of the function we are taking the inverse of. let y=1+2sin(3x)so now, x=1+2sin(3y)Aiming to make y the subject, x-1= 2sin(3y)Therefore, (x-1)/2=sin(3y), 3y= ar...
HC
Answered by Harry C. • Maths tutor
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y = 4sin(x)cos(3x) . Evaluate dy/dx at the point x = pi.

By product rule:u = 4sin(x) v = cos(3x)du/dx = 4cos(x) dv/dx = -3sin(3x)dy/dx = u (dv/dx) + v (du/dx)dy/dx = 4sin(x) * -3sin(3x) + cos(3x) * 4cos(x)dy/dx = -12sin(x)sin(3x) + 4cos(x)cos(3x)Evaluate at x = pi...
WF
Answered by Will F. • Maths tutor
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What is a logarithm?

We can explain this by taking a simple power equation such as 2 3 = 8 and setting each number as an unknown variable. For instance 2 3 = x is solved by cubing 2, x 3 = 8 is solved by taking the cube root of ...
DW
Answered by Daniel W. • Maths tutor
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Use integration to find the exact value of [integral of] (9-cos^2(4x)) dx

you cannot integrate cos^2(4x) without making substitutions first. Use the cos^2(x) + sin^2(x) = 1 identity with the cos(2x)=cos^2(x)-sin^2(x), rearrange to get the identity cos(2x) = 2cos^2(x) - 1, then cos...
AF
Answered by Anna F. • Maths tutor
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Solve the equation sec^2(A) = 3 - tan(A), for 0<= A <= 360 (degrees)

Using simple trig identities, we know tan^2(A) + 1 = sec^2(A).Substituting for sec^2(A) into our equation, we get: tan^2(A) + 1 = 3 - tan(A).Moving this over to one side, we get the quadratic in terms of tan...
LF
Answered by Lachlan F. • Maths tutor
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