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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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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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Of the following 4 equations, 3 of them represent parallel lines. Which is the odd one out?

2y - 3x = 4 2) -12x = 4(1 - 2y) 3) y - 5 = 3(x - 1)/2 4) 3(y - x) = 4 - y This question relies on the student's understanding of parallel lines as well as their ability to rearrange equations. The key piece ...
WS
Answered by Wayne S. • Maths tutor
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Find the equation of the normal to the curve y = 2x^2 -3x +7 at the point x = 1.

Thinking about the normal, it is a line which cuts the curve at right angles, and so will have the form y = mx + c. Now at the point where x = 1, we know the y value from the curve's equation is y = 2(1) 2 -...
MJ
Answered by Matthew J. • Maths tutor
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