What is the general solution for cos(8t)-5sin(8t)=0 ?

The general solution for cos(8t)-5sin(8t)=0 is t=(0.19739…)/8+(pin)/8

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cos(8t)-5sin(8t)=0

cos (8 t) - 5 sin (8 t) = 0

t = \frac{0.19739 \dots}{8} + \frac{πn}{8}

Solution steps

cos (8 t) - 5 sin (8 t) = 0

Rewrite using trig identities

1 - 5 tan (8 t) = 0

Move

1

to the right side

- 5 tan (8 t) = - 1

Divide both sides by

- 5

tan (8 t) = \frac{1}{5}

Apply trig inverse properties

8 t = arctan (\frac{1}{5}) + πn

Solve

8 t = arctan (\frac{1}{5}) + πn : t = \frac{arctan ( \frac{1}{5} )}{8} + \frac{πn}{8}

t = \frac{arctan ( \frac{1}{5} )}{8} + \frac{πn}{8}

Show solutions in decimal form

t = \frac{0.19739 \dots}{8} + \frac{πn}{8}

cos^{2} (x) + 3 sin (x) + 1 = 0

\frac{a ^{0.2}}{( cos ^{2} ( x ) ) - cos ^{2} ( x ) - 1} = 0

(\frac{2 cos ( x )}{2 - 1}) (\frac{sin ( x )}{2 + 2}) = 0

4 cos^{2} (x) + 17 sin (x) = 8

cos^{4} (x) = 1 - 8 sin^{2} (x) cos^{2} (x)

What is the general solution for cos(8t)-5sin(8t)=0 ?
The general solution for cos(8t)-5sin(8t)=0 is t=(0.19739…)/8+(pin)/8