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Consider an isosceles triangle ABC, where AB=AC=1, M is the midpoint of BC, and <BAM=<CAM=x. Use trigonometry to find an expression for BM and by finding BC^2, show that cos2x = 1 - 2(sinx)^2.

Consider the right-angled triangle BAM. We have the hypotenuse and an angle, and want to find the opposite side. Therefore, using SOHCAHTOA, sinx = BM/1, hence BM = sinx. Because M is the midpoint of BC, ...

Answered by Blessie S. Maths tutor
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Solve 5x + 10 = 2x(5x + 10)

First multiply out the right hand side to get5x + 10 = 10x^2 + 20xThen rearrange so everything equals zero, forming a quadratic equation10x^2 + 15x - 10 = 0 To make things easier, you can simplify the equ...

Answered by Amy M. Maths tutor
3513 Views

Sketch the function (x^4 + 2x^3 - x -2)/(x+2)

First of all determine the range of the function by looking at its denominator. The function is defined at each point except x=-2 Now to find the zeros o...

Answered by Matteo D. Maths tutor
2538 Views

Find the equation of the tangent for x = 2cos (2y +pi)

So this initially looks like a tricky question- especially the way it is written in the form of x as a function of y, ( x(y) ), rather than what we normally see y as a function of x, ( y(x) ).The first th...

Answered by Tonia M. Maths tutor
2978 Views

Solve the simultaneous equations 3x + y = –4 and 3x – 4y = 6

  1. Label first equation as equation 1 and the second as equation 22) Make y the subject of the equation from equation (1); hence: eq 1 : y = -4 -3x3) Substitute the new equation into equation (2) : 3x-...
Answered by Munachi I. Maths tutor
2565 Views

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