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Find all possible values of θ for tan θ = 2 sin θ with the range 0◦ ≤ θ ≤ 360◦

First you rearrange the equation.It is known that tanθ=sinθ/cosθ therefore if we replace tanθ with sin/cos we get:sinθ/cosθ=2sinθIf you multiply both sides by cosθ this becomes:sinθ=2sinθcosθThen if you minu...
KL
Answered by Kehinde L. • Maths tutor
10849 Views

Find ∫ (2x^5 - 1/(4x^3)-5) dx. giving each term in its simplest form.

with integration you need to increase the power and divide through by the new power for each term in the equation.2x 5 goes to 2x 6 /6 = x 6 /3-1/(4x 3 ) is equal to -x -3 /4 which then goes to -x -2 /4/-2 =...
KY
Answered by Kieran Y. • Maths tutor
6441 Views

Find both stationary points for y= 4x^(3)-3x^(2)-60x+24. Also find the nature of those points.

y= 4x 3 - 3x 2 - 60x+ 24dy/dx = 12x 2 - 6x- 60 = 2x 2 - x- 10 = (2x-5)(x+2) So stationary points are at x= 5/2 and x= -2 d 2 x/dy 2 = 24x - 6 24(5/2) - 6 = positive so this is a minimum point 24(-2) - 6 = ne...
WM
Answered by Will M. • Maths tutor
7156 Views

Find the coordinates of the points where the lines y=x^2-5x+6 and y=x-4 intersect.

At the points of intersection the x and y coordinates will be the same. So we can solve the equations simultaneously to see what solutions to x and y solve both equations.Rearrange the second equation to get...
GC
Answered by Georgia C. • Maths tutor
6549 Views

what does it mean if "b^2 - 4ac < 0" for a quadratic equation (eg y = a*x^2 + b*x + c)

The question comes from the quadratic equation r = (-b +- sqrt(b 2 - 4ac)/2a where r is the root or x coordinate where the line crosses the x-axsis (the y coordinate is always 0). If b 2 - 4ac &lt; 0 then to...
NW
Answered by Nick W. • Maths tutor
6038 Views