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Express 2cos(x) + 5sin(x) in the form Rsin(x + a) where 0<a<90

Expanding Rsin(x + a): Rsin(x + a) = Rsin(x)cos(a) + Rcos(x)sin(a) Comparing coefficients of sin(x), cos(x) with first expression leads to: Rsin(a) = 2, Rcos(a) = 5 Dividing these equations gives: tan(a) = 2...
DH
Answered by Dan H. • Maths tutor
12386 Views

A girl kicks a ball at a horizontal speed of 15ms^1 off of a ledge 20m above the ground. What is the horizontal displacement of the ball when it hits the ground?

As we are looking for the horizontal displacement first we look at horizontal motion. We know that the horizontal velocity is 15ms^-1 but we dont know the time so we can't work out the horizontal displacemen...
VW
Answered by Victoria W. • Maths tutor
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Differentiate tan^2(x) with respect to x

d/dx(tan^2(x)) is not a known differential, and therefore requires a substitution to calculate it using simpler known differentials. Using the identity sin^2(x) + cos^2(x) = 1, the equation can be divided th...
HA
Answered by Harry A. • Maths tutor
22837 Views

By first proving that sin2θ=2sinθcosθ, calculate ∫1+sinθcosθ dθ.

We have, from the formula book, sin⁡(A±B)=sinAcosB±cosAsinB Using A=B=θ , we have sinθ+θ=sinθcosθ+cosθsinθ Which we can simplify to sin2θ=2sinθcosθ as required. We can then substitute this into the integral:...
AH
Answered by Abigail H. • Maths tutor
7663 Views

How would we evaluate (1/3)^-3/2 ?

When evaluating more complex exponentials it is helpful to break them up into smaller steps. so when we are aproched with (1/3) -3/2 we should first look at the effect that the negative sighn has on the frac...
RR
Answered by Riley R. • Maths tutor
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