Core 3: Find all the solutions of 2cos(2x) = 1-2sin(x) in the interval 0<x<360
2cos(2x) = 1-2sin(x)
2(1-2sin2(x)) = 1-2sin(x) -- by our trigonometric functions
2-4sin2(x) = 1-2sin(x)
4sin2(x)-2sin(x)-1=0 -- rearrange
sin(x) = (2±(4-4(4)(-1))0.5)/8 -- quadratic formula
x = 54 & x = -18 which on the range 0
CB
Related Maths A Level answers
All answers ▸Find the exact solution, in its simplest form, to the equation ln(4y + 7) = 3 + ln(2 – y) (Core Maths 3 Style Question)
Find the solutions of the equation: sin(x - 15degrees) = 0.5 between 0<= x <= 180
How do I find the integral ∫(ln(x))^2dx ?
A curve has the equation: x^3 - x - y^3 - 20 = 0. Find dy/dx in terms of x and y.