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Integrate Cos^2(x)

{} = integral sign for purpose of this solutioncos 2 x = 1 - sin 2 x (1)cos 2x = cos 2 x - sin 2 x (2)cos 2 x = 1 - (cos 2 x - cos 2x)cos 2 x = 1 - cos 2 x + cos 2x2 cos 2 x = 1 + cos 2xcos 2 x = (1 + cos 2x...
RS
Answered by Ryan S. • Maths tutor
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A triangle has sides a,b,c and angles A,B,C with a opposite A etc. If a=4,b=3,A=40, what is the area of the triangle?

First use the sine rule (that a/sin(A)=b/sin(B)=c/sin(C)) to find the value of B. a/sin(A)=b/sin(B) so B=arcsin(b sin(A)/a) which is approximately equal to 28.82. Since the angles of a triangle have 180 degr...
Answered by • Maths tutor
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x is an angle, if 180 > x > 90 and sinx = √2 / 4 what is the value of angle x

sin-1(√2 / 4 ) = 20.7•Looking at a sin graph this is also true at 180-20.7 = 159.3•x = 159.3•
MQ
Answered by Matilda Q. • Maths tutor
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If y = 4x^3 - 6x^2 + 7 work out dy/dx for this expression

y = 4x^3 - 6x^2 + 7 dy/dx = 12x^2 -12x
MQ
Answered by Matilda Q. • Maths tutor
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How do you find the distance a ball travels if fired at speed u and angle theta from the ground?

From a right angled triangle with hypotenuse u and angle theta, we see the horizontal speed is (u cos theta) and the initial vertical speed is (u sin theta). As the ball moves in a symmetric parabola, it hit...
DB
Answered by Douglas B. • Maths tutor
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