2cos(4θ+20)=0.8

Solution

2 cos (4 θ + 20) = 0.8

θ = - 5 + \frac{πn}{2} + \frac{1.15927 \dots}{4}, θ = \frac{π}{2} + \frac{πn}{2} - \frac{1.15927 \dots}{4} - 5

Solution steps

2 cos (4 θ + 20) = 0.8

Divide both sides by

2

cos (4 θ + 20) = 0.4

Apply trig inverse properties

4 θ + 20 = arccos (0.4) + 2 πn, 4 θ + 20 = 2 π - arccos (0.4) + 2 πn

Solve

4 θ + 20 = arccos (0.4) + 2 πn : θ = - 5 + \frac{πn}{2} + \frac{arccos ( 0.4 )}{4}

Solve

4 θ + 20 = 2 π - arccos (0.4) + 2 πn : θ = \frac{π}{2} + \frac{πn}{2} - \frac{arccos ( 0.4 )}{4} - 5

θ = - 5 + \frac{πn}{2} + \frac{arccos ( 0.4 )}{4}, θ = \frac{π}{2} + \frac{πn}{2} - \frac{arccos ( 0.4 )}{4} - 5

Show solutions in decimal form

θ = - 5 + \frac{πn}{2} + \frac{1.15927 \dots}{4}, θ = \frac{π}{2} + \frac{πn}{2} - \frac{1.15927 \dots}{4} - 5

2 - 2 cos^{2} (\frac{x}{2}) = sin^{2} (x)

sin (θ) = \frac{2}{2}, 0 \leq θ \leq 2 π

x, cos (x) = \frac{2}{3}

3 sin (x) + 2 = 1.5

3 sec^{2} (x) - 2 tan (x) - 4 = 0