Top answers

Solve 4cos(2x )+ 2sin(2x) = 1 given -90° < x < 90°. Write 4cos(2x )+ 2sin(2x) in the form Rcos(2x - a), where R and a are constants.

Step 1: Recognise 4cos(2x )+ 2sin(2x) must be put into the form given in the question form i.e. Rcos(2x - a) as it contains only one trigonometric function Step 2: Calculate values of R and a a. Expand Rcos(...
PK
Answered by Prannay K. • Maths tutor
17782 Views

If cos(x)= 1/3 and x is acute, then find tan(x).

Consider a right angled triangle. Call one of the angles (not the right angle) in this triangle x. We can do this as we are told x is acute. The side opposite to x label O, the side adjacent to x label A, an...
HK
Answered by Hugh K. • Maths tutor
19342 Views

If n is an integer prove (n+3)^(2)-n^(2) is never even.

Let us begin by simplifying the expression:(n+3) 2 - n 2 = (n+3)(n+3) - n 2 = n 2 + 6n + 9 - n 2 (expanded brackets)= 6n + 9 (collected like terms)= 3(2n+3) (taken out a factor of 3)Now we can consider this ...
HK
Answered by Hugh K. • Maths tutor
7709 Views

For what values of k does the graph y=x^(2)+2kx+5 not intersect the x-axis

Where the graph intersects the x-axis, x 2 +2kx+5 must be equal to zero. Thus we can answer the equivalent question: For what k does x 2 +2kx+5 = 0 not have a solution?This is now a simpler problem (roots of...
HK
Answered by Hugh K. • Maths tutor
30475 Views

How do you do integration by parts?

When you see a complicated product, split it into the form u.v', where u and v' are algebraic expressions such as x^2. You can then use the formula: uv'=uv-integral(vu') which you would take between any limi...
AB
Answered by Andrew B. • Maths tutor
3571 Views