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Write 5cos(theta) – 2sin(theta) in the form Rcos(theta + alpha), where R and alpha are constants, R > 0 and 0 <=alpha < 2 π Give the exact value of R and give the value of alpha in radians to 3 decimal places.

Use the formula cos(A+B)=cosAcosB-sinAsinB, Rcos(theta+alpha)=Rcos(alpha)cos(theta)-Rsin(alpha)sin(theta)5=Rcos(alpha)2=Rsin(alpha)tan(alpha)=2/5alpha= 0.381R=sqrt(5^2+2^2)=sqrt(29)So, 5cos(theta) – 2sin(...

Answered by Joe W. • Maths tutor

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The equation of the line L1 is y = 3x – 2 The equation of the line L2 is 3y – 9x + 5 = 0 Show that these two lines are parallel.

L1 is in the form y=mx+c where m is the gradient, 3.L2 can be rewritten as 3y=9x-5, then y=3x-(5/3) to reach y=mx+c. So, the gradient of L2 is 3.Therefore, both lines are parallel.

Answered by Joe W. • Maths tutor

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The angles of a triangle are a, 2a and 2a + 30. Work out the value of a.

The areas of a triangle add up to 180 degrees. Therefore to tackle this question you must use algebra as you know that the sum of a, 2a and 2a + 30 is 180. a + 2a + 2a + 30 = 180 All the like terms can be...

Answered by Amy G. • Maths tutor

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Find dy/dx for y=5x^3−2x^2+7x−15

'Find dy/dx' means it wants us to differentiate. The rules for this are multiply the coefficient (number before x) by the current power, then decrease the power by 1.In this example:5x³ would b...

Answered by Georgia S. • Maths tutor

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y= arcos(x). Find dy/dx in terms of x.

Rearrange the expression to create a familiar function with a known differencial: arcos(x)=y x= cos(y) Differenciate x with respect to y: dx/dy= -sin(y) We know that dy/dx= 1/(dx/dy), so rearange to find ...

Answered by Danyal K. • Maths tutor

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