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What is a good way to remember the sine, cosine and tangent rules of a triangle?

If you are trying to find the sine of an angle, remember: SOH The sine of an angle (S)= the length of the opposite side (O) / the length of the hypotenuse (H) If you are trying to find the cosine of an angle...
HW
Answered by Hannah W. • Maths tutor
4438 Views

Share £650 in the ratio 8:5

Begin by adding the 2 ratio parts (i.e. the numbers which make up the ratio) so 8+5 = 13. Then divide the total sum by the sum of the ratio parts. Thus £650/13 = £50. Multiply this by each of the ratio parts...
HV
Answered by Harry V. • Maths tutor
8048 Views

Integrate 1/(5-2x) for 3≤x≤4

You must be careful with these sorts of questions as although 1/(5-2x) is equivalent to (5-2x)^-1, when you integrate you would add one to the power and divide by the new power. But if you were to add one to...
ES
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Using the addition formula for sin(x+y), find sin(3x) in terms of sin(x) and hence show that sin(10) is a root of the equation 8x^3 - 6x + 1

First we state the formula for sin(x+y) sin(x+y) = sin(x)cos(y) + cos(x)sin(y) Letting y = 2x sin(x+2x) = sin(x)cos(2x) + cos(x)sin(2x) Now sin(2x) = 2sin(x)cos(x) and cos(2x) = 1 - 2sin^2(x), substitute the...
KR
Answered by Kyle R. • Maths tutor
22871 Views

Using Integration by Parts, find the indefinite integral of ln(x), and hence show that the integral of ln(x) between 2 and 4 is ln(a) - b where a and b are to be found

Using integration by parts, we can re-write the integral of ln(x) as (x ln(x) - int(x (1/x))) = x*ln(x) - x Therefore, evaluating between 2 and 4 gives us (4 ln(4) - 4) - (2 ln(2) - 2) = 2ln(16/2) - 4 + 2 = ...
KR
Answered by Kyle R. • Maths tutor
4253 Views