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Integrate Sin^2(x)

(using double angle formula)Sin^2(x)=1/2-(Cos(2x)/2) So the Integral is 1/2(x-1/2Sin(2x))which simplifies to x/2 - 1/2Sin(x)Cos(x)
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Answered by Alex R. • Maths tutor
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The perimeter of a right-angled triangle is 72 cm. The lengths of its sides are in the ratio 3 : 4 : 5. Work out the area of the triangle.

Consider a right angled triangle, it has perimeter of 72cm. Let's label the three sides a, b and c.Therefore, a + b + c = 72cm.Also, we know that a:b:c = 3:4:5Therefore we can say that a = 3x, b = 4x, c = 5x...
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Answered by Dilan A. • Maths tutor
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Express 6cos(2x)+sin(x) in terms of sin(x). Hence solve the equation 6cos(2x) + sin(x) = 0, for 0° <= x <= 360°.

Firstly, we need to express 6cos(2x) + sin(x) in terms of sin(x) 6cos(2x) + sin(x) = 6cos(x+x) + sin(x) = 6cos 2 (x) - 6sin 2 (x) + sin(x) (applying cos(x+y) = cos(x)cos(y) - sin(x)sin(y)) = 6(1 - sin 2 (x))...
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Answered by Dilan A. • Maths tutor
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A curve has equation x^2 +2xy–3y^2 +16=0. Find the coordinates of the points on the curve where dy/dx = 0.

x 2 +2xy–3y 2 +16=0Differentiate the terms:x 2 gives 2x2xy is differentiated by the product rule: vu' +v'u Make v = 2x and u = y, which gives 2x(dy/dx) + 2y3y 2 gives 6y(dy/dx)16 gives 0.Therefore we have th...
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Answered by Dilan A. • Maths tutor
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Solve the following simulatenous equation to find the values of both x and y: 5x+2y=16 3x-y=14

x=4, y=-2
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Answered by Oliver G. • Maths tutor
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