What is the general solution for 5tan(θ)-4=0 ?

The general solution for 5tan(θ)-4=0 is θ=0.67474…+pin

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5tan(θ)-4=0

5 tan (θ) - 4 = 0

θ = 0.67474 \dots + πn

Degrees

θ = 38.65980 \dots^{\circ} + 18 0^{\circ} n

Solution steps

5 tan (θ) - 4 = 0

Move

4

to the right side

5 tan (θ) - 4 = 0

Add

4

to both sides

5 tan (θ) - 4 + 4 = 0 + 4

Simplify

5 tan (θ) = 4

5 tan (θ) = 4

Divide both sides by

5

5 tan (θ) = 4

Divide both sides by

5

\frac{5 tan ( θ )}{5} = \frac{4}{5}

Simplify

tan (θ) = \frac{4}{5}

tan (θ) = \frac{4}{5}

Apply trig inverse properties

tan (θ) = \frac{4}{5}

General solutions for

tan (θ) = \frac{4}{5}

tan (x) = a \Rightarrow x = arctan (a) + πn

θ = arctan (\frac{4}{5}) + πn

θ = arctan (\frac{4}{5}) + πn

Show solutions in decimal form

θ = 0.67474 \dots + πn

0 = cos (\frac{x}{2})

3 cos (x) - 1 = cos (2 x)

7 cos^{2} (θ) - 9 = - 9 sin (θ)

y, arcsin (y) = x

- 4 cos (2 θ) - 3 cos (θ) - 4 = - 2 cos (θ) - 7

What is the general solution for 5tan(θ)-4=0 ?
The general solution for 5tan(θ)-4=0 is θ=0.67474…+pin