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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 = sin²(θ) +cos²(θ)/ sin(θ)cos(θ). Since, s...

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 k...

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)<...

Answered by Matthew J. • Maths tutor

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A curve with equation y=f(x) passes through point P at (4,8). Given that f'(x)=9x^(1/2)/4+5/2x^(1/2)-4 find f(X).

To find f(x) using its derivative, first integrate f'(x) with respect to x using the 'add one to the power and divide by the new power' technique remembering to add the constant c. To make this easier, tu...

Answered by Em C. • Maths tutor

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Integrate the function y = 2x^2 + 3x + 8 with respect to x.

Answer = 2x^3/3 + 3x^2/2 + 8x + CThis is an example of numerical integration from C1. To begin to answer this question, we can integrate each term at a time. To integrate this function, we raise the power...

Answered by Michael C. • Maths tutor

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