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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
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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
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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
7670 Views

The size of two of the three angles in a triangle are 40 degrees and 70 degrees. What is the special name given to this triangle?

It is an isosceles triangle. We know this because 40 + 70 = 110. So we take away 110 from 180 (The sum of the three degrees in a triange) to give us the degree of the last angle, which is 70. Since we have t...
NR
Answered by Natalie R. • Maths tutor
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