Solve 4 cos^2(\theta ) - 3 = 0

Evaluate

4 cos^{2} (θ) - 3 = 0

Add or subtract both sides

4 cos^{2} (θ) = 3

Divide both sides

\frac{4 cos ^{2} ( θ )}{4} = \frac{3}{4}

Divide the numbers

cos^{2} (θ) = \frac{3}{4}

Take the root of both sides of the equation and remember to use both positive and negative roots

cos (θ) = \pm \frac{3}{4}

Simplify the expression

cos (θ) = \pm \frac{3}{2}

Separate the equation into 2 possible cases

cos (θ) = \frac{3}{2} cos (θ) = - \frac{3}{2}

Calculate

More Steps

θ = {\frac{π}{6} + 2 kπ \frac{11 π}{6} + 2 kπ, k \in Z cos (θ) = - \frac{3}{2}

Calculate

More Steps

θ = {\frac{π}{6} + 2 kπ \frac{11 π}{6} + 2 kπ, k \in Z θ = {\frac{5 π}{6} + 2 kπ \frac{7 π}{6} + 2 kπ, k \in Z

Solution

θ = {\frac{π}{6} + kπ \frac{5 π}{6} + kπ, k \in Z

Alternative Form

θ = {3 0^{\circ} + 18 0^{\circ} k 15 0^{\circ} + 18 0^{\circ} k, k \in Z

Alternative Form

θ \approx {0.523599 + kπ 2.617994 + kπ, k \in Z

Solve the equation