What is the general solution for 2sin^2(t)-cos(t)=1 ?

The general solution for 2sin^2(t)-cos(t)=1 is t=pi+2pin,t= pi/3+2pin,t=(5pi)/3+2pin

Popular >

2sin^2(t)-cos(t)=1

2 sin^{2} (t) - cos (t) = 1

t = π + 2 πn, t = \frac{π}{3} + 2 πn, t = \frac{5 π}{3} + 2 πn

Solution steps

2 sin^{2} (t) - cos (t) = 1

Subtract

1

from both sides

2 sin^{2} (t) - cos (t) - 1 = 0

Rewrite using trig identities

1 - cos (t) - 2 cos^{2} (t) = 0

Solve by substitution

cos (t) = - 1, cos (t) = \frac{1}{2}

cos (t) = - 1 : t = π + 2 πn

cos (t) = \frac{1}{2} : t = \frac{π}{3} + 2 πn, t = \frac{5 π}{3} + 2 πn

Combine all the solutions

t = π + 2 πn, t = \frac{π}{3} + 2 πn, t = \frac{5 π}{3} + 2 πn

4 sin^{2} (x) + 4 sin (x) = - 1

sin (θ) = \frac{8}{17}, cos (θ)

θ, 3 cos (θ - 5 5^{\circ}) = - 1.56

- 6 sin (c) - 12 = 2 sin (c) - 4

x, 3 cot^{2} (x) - 1 = 0

What is the general solution for 2sin^2(t)-cos(t)=1 ?
The general solution for 2sin^2(t)-cos(t)=1 is t=pi+2pin,t= pi/3+2pin,t=(5pi)/3+2pin