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Express cos(x) + (1/2)sin(x) in terms of a single resultant sinusoidal wave of the form Rsin(x+a)

cos(x) + (1/2)sin(x) : Rsin(x + a) = R{sin(x)cos(a) + cos(x)sin(a)} = (1/2)sin(x) + (1)cos(x) (comparing coeffs.) Therefore Rcos(a) = 1/2 and separately Rsin(a) = 1 So tan(a) = 2 and R^2 = 5/4. Answer: sqrt(...
HT
Answered by Hakkihan T. • Maths tutor
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Find the general solution, in degrees, of the equation 2 sin(3x+45°)= 1

A general way of solving these equations is getting them to the form sin(y)=k . In this case, to do so, we have to divide by 2 and then put y=3x+45° We then get sin(y)=1/2 . You should know which angles have...
CG
9385 Views

The quadratic equation 2x^2+ 6x+7 has roots a and b. Write down the value of a+b and the value of ab.

A general method would be to compute a and b with the general solution formula for quadratic equations. However, a special property of quadratic equations can make this a lot easier. In fact, given the equat...
CG
6339 Views

Define hard engineering in the context of coastal managment

Hard engineering is a method of coastal management that involves the building of large and generally expensive features in order to defend against the sea,this usually includes building sea walls, groynes, a...
LW
5519 Views

state the difference between a normal and a reverse fault

A normal fault is a fault that involves extensional movement along its fault plane, this involves the hanging wall moving down in relation to the footwall. A reverse fault involves contraction along its faul...
LW
Answered by Laurence W. • Geology tutor
10233 Views