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(Core 3 level) Integrate the function f(x) = 2 -cos(3x) between the bounds 0, pi/3.

f(x) = 2 - cos(3x)integrate function x term2 -> 2x (raise power of x then divide by new power for polynomial functions of x) -cos(3x) -> -(1/3)(sin(3x)) (using a substitution of 3x = u, then cos(u) int...
RG
Answered by Riku G. • Maths tutor
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How do I work out if two lines are parallel?

The gradients of the two lines must be the same. The gradient is m in the equation: y=mx+c For example: L1: y = 3x – 2L2: 3y – 9x + 5 = 0 First rearrange L2 so it is in the same form as L1 to get:3y=9x-5Then...
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Answered by Alexandra B. • Maths tutor
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What is the value of sin(theta), cos(theta), tan(theta) where theta = 0, 30, 45, 60, 90

sin(0) = 0 ; sin(30) = 1/2; sin(45) = 1/sqrt(2); sin(60) = sqrt(3)/2; sin(90) = 1cos(0) = 1; cos(30) = sqrt(3)/2; cos(45) = 1/sqrt(2); cos(60) = 1/2; cos(90) = 0 tan(0) = 0; tan(30) = 1/sqrt(3); tan(45) = 1;...
LB
Answered by Luqman B. • Maths tutor
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(i) Prove sin(θ)/cos(θ) + cos(θ)/sin(θ) = 2cosec(2θ) , (ii) draw draph of y = 2cosec(2θ) for 0<θ< 360°, (iii) solve to 1 d.p. : sin(θ)/cos(θ) + cos(θ)/sin(θ) = 3.

For (i) Start by looking at left hand side of the equation. It is usually much easier to reduce large expression into smaller ones. So, LHS = sin 2 (θ) +cos 2 (θ)/ sin(θ)cos(θ). Since, sin 2 (θ) +cos 2 (θ) =...
RK
Answered by Rabin K. • Maths tutor
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The equation of line L is y= 3x+2 and the equation of line M is 3y–9x+5=0. Show that these lines are parallel.

First step is to understand what it means for lines to be parallel. This is when the gradients of two lines are the same.This is much easier to see when the format of the equations is the same, so lets rearr...
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Answered by Paulius P. • Maths tutor
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