What is the general solution for 8cos(2t)-14sin(2t)=0 ?

The general solution for 8cos(2t)-14sin(2t)=0 is t=(0.51914…)/2+(pin)/2

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8cos(2t)-14sin(2t)=0

8 cos (2 t) - 14 sin (2 t) = 0

t = \frac{0.51914 \dots}{2} + \frac{πn}{2}

Solution steps

8 cos (2 t) - 14 sin (2 t) = 0

Rewrite using trig identities

8 - 14 tan (2 t) = 0

Move

8

to the right side

- 14 tan (2 t) = - 8

Divide both sides by

- 14

tan (2 t) = \frac{4}{7}

Apply trig inverse properties

2 t = arctan (\frac{4}{7}) + πn

Solve

2 t = arctan (\frac{4}{7}) + πn : t = \frac{arctan ( \frac{4}{7} )}{2} + \frac{πn}{2}

t = \frac{arctan ( \frac{4}{7} )}{2} + \frac{πn}{2}

Show solutions in decimal form

t = \frac{0.51914 \dots}{2} + \frac{πn}{2}

1 - 2 sin (θ) = 0

sin^{2} (x) = 2 cos (x)

2 cos^{2} (θ) + 4 sin (θ) - 13 = 9 sin (θ) - 9

cot (θ) = - \frac{5}{4}

tan^{2} (θ) + 5 tan (θ) = 0

What is the general solution for 8cos(2t)-14sin(2t)=0 ?
The general solution for 8cos(2t)-14sin(2t)=0 is t=(0.51914…)/2+(pin)/2