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Show, by counter-example, that the statement "If cos(a) = cos(b) then sin(a) = sin(b)" is false.

Let a=60 and b=300. Then cos(a)=cos(60)=0.5 and cos(b)=cos(300)=0.5, therefore cos(a)=cos(b). Then sin(a)=sin(60)=sqrt(3)/2 and sin(b)=sin(300)=-sqrt(3)/2, therefore sin(a)=sin(b) is incorrect. Therefore we ...
OG
Answered by Osian G. • Maths tutor
4891 Views

Differentiate y(x)=x^2 + 2x + 1, find the turning point and classify it as minimum or maximum.

dy/dx=2x + 2 Turning point is where dy/dx=0, so when x = -1 When x=-1, y=0. d^2y/dx^2=2 > 0 therefore minimum.
JF
Answered by John F. • Maths tutor
4550 Views

Differentiate (3x)e^(3x)

3e^3x + (9x)e^3x This is a good question because it involves the use of both the chain and product rules of differentiation, as well as the differential of e (all of which occur frequently in Maths A-level a...
JH
Answered by Joe H. • Maths tutor
4650 Views

The second term of an arithmetic sequence is 7. The sum of the first four terms of the arithmetic sequence is 12. Find the first term, a, and the common difference, d, of the sequence.

Let a be the first term Let d be the common difference a + d = 7 S 4 = 4/2 (2a +3d) = 12 Simultaneous equation: a+d =7 // x 6 4a +6d = 12 Difference btween these two 6a + 6d = 42 4a +6d = 12 2a = 30 a = 15 d...
AT
Answered by Alexander T. • Maths tutor
22118 Views

Integrate 5cos(3x - 1) with respect to x

Firstly, we may simplify the expression by factoring out any constants. In this case 5 can be factored out. 5 ∫ cos(3x-1) dx For the integrand cos(3x -1), we can use a simple u-substitution. Where u = 3x -1 ...
RM
Answered by Rian M. • Maths tutor
6080 Views