Solve for -pi < x < pi: tanx = 4cotx + 3
tanx = 4cotx + 3 - Multiply through by tan to form a quadratic. tan^2x = 4 + 3tanx - Simplify by allowing y to equal tanx. y^2 = 4 + 3y - Rearange to standard quadratic form. y^2 - 3y -4 = 0 - Factorise. (y - 4)(y + 1) = 0 Therefore y = 4 and y = -1 Substitute y=tanx to solve for x: y = 4 tanx = 4 x = tan-14 x= 1.326 (3d.p.) tanx = -1 x = tan-1 -1 x = -pi/4
ZL
Related Maths A Level answers
All answers ▸How do you find the gradient of a line?
i) Using implicit differentiation find dy/dx for x^2 + y^2 = 4 ii) At what points is the tangent to the curve parallel to the y axis iii) Given the line y=x+c only intersects the circle once find c given that c is positive.
How do you differentiate y = 5 x^3 + 1/2 x^2 + 3x -4
Differentiate 2e^(3x^2+6x)