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Core 3: Find all the solutions of 2cos(2x) = 1-2sin(x) in the interval 0<x<360

2cos(2x) = 1-2sin(x) 2(1-2sin 2 (x)) = 1-2sin(x) -- by our trigonometric functions 2-4sin 2 (x) = 1-2sin(x) 4sin 2 (x)-2sin(x)-1=0 -- rearrange sin(x) = (2±(4-4(4)(-1)) 0.5 )/8 -- quadratic formula x = 54 &a...
CB
Answered by Chris B. • Maths tutor
9311 Views

How would I differentiate something with the product rule?

Okay so, first of all the product rule in itself is fairly simple. Take the product of a function &quot;u&quot; and a function &quot;v&quot; to be a compound function. You can write this as &quot;uv&quot;. T...
SD
Answered by Shivam D. • Maths tutor
4040 Views

How would I solve the equation 25^x = 5^(4x+1)?

You would have to rewrite 25 as 5^2 hence 25^x = (5^2)^x = 5^(2*x). Then 5^(2x) = 5^(4x+1) and therefore 2x = 4x + 1 hence 2x = -1 hence x = -1 / 2.
MP
Answered by Marius P. • Maths tutor
9433 Views

Prove the identity (4cos(2x))/(1+cos(2x)) = 4-2sec^2(x)

Write down the formulas involving cos2x and select the one which involves only cosine, this is because cosine (or derivations of it) is the only trigonometric function in this question. Substitute the chosen...
TN
Answered by Tegan N. • Maths tutor
14193 Views

Solve the differential equation: dy/dx = 6x^2 + 4x + 9

dy/dx = 6x 2 + 4x + 9 dy = (6x 2 + 4x + 9) dx integrating gives: y= (6x 3 /3) + (4x 2 /2) + 9x + c y= 2x 3 + 2x 2 + 9x + c If given boundary conditions of y(0)=0 then 0 = 2(0) 3 + 2(0) 2 +9(0) +c therefore c...
JH
Answered by Jack H. • Maths tutor
11548 Views