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Show how '2sin(x)+sec(x+ π/6)=0' can be expressed as √3sin(x)cos(x)+cos^2(x)=0.

To do this question we must first be aware of a few trigonometric identities. 1. sec(x) = 1/cos(x). 2. cos(A + B) = cos(A)cos(B) - sin(A)sin(B). (double angle formula) 3 . sin^2(x) = 1 - cos^2(x) Before divi...
RP
Answered by Ruadhan P. • Maths tutor
10576 Views

How do you find the integral of 'x sin(2x) dx'?

To begin, notice that the expression involves 2 functions of x multiplied together, this means we can approach the problem using integration by parts. Integration by parts can be expressed as '∫ u (dv/dx) dx...
RP
Answered by Ruadhan P. • Maths tutor
23723 Views

Use Simpson’s Rule with five ordinates to find an approximate value for the integral e^(x^2)dx between the values of 0 and 1

Find the value of dx by dividing the difference between the integral boundaries by the number of ordinates minus 1. Therefore dx=(1-0)/4=1/4. Then define your ordinates, by 5 values between 0 and 1, where th...
JF
Answered by Joshua F. • Maths tutor
7566 Views

Express 4sinx + 3cosx in the form Rcos(x-a)

From the following identity, cos(a-b) = cosacosb+ sinasinb, we find that 4sinx+3cosx = R(cosxcosa+sinxsina). We now equate the coefficients: 3 = Rcosa and 4=Rsina. Using basic trigonometry, we can make this ...
DT
Answered by Dorothy T. • Maths tutor
21877 Views

Solve |3x+1| = 1

Firstly square both sides. This way, we now know that both sides have to be positive (3x+1)^2 = 1 (3x+1)(3x+1) = 1 Expand the quadratic... 9x^2 + 12x + 4 = 1 9x^2 + 12x + 3 = 0 Now complete the square. First...
DT
Answered by Dorothy T. • Maths tutor
7906 Views