What is the general solution for 15tan(θ)-7=5tan(θ)-3 ?

The general solution for 15tan(θ)-7=5tan(θ)-3 is θ=0.38050…+pin

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Popular Trigonometry >

15tan(θ)-7=5tan(θ)-3

Solution

15 tan (θ) - 7 = 5 tan (θ) - 3

Solution

θ = 0.38050 \dots + πn

Degrees

θ = 21.80140 \dots^{\circ} + 18 0^{\circ} n

Solution steps

15 tan (θ) - 7 = 5 tan (θ) - 3

Solve by substitution

15 tan (θ) - 7 = 5 tan (θ) - 3

Let:

tan (θ) = u

15 u - 7 = 5 u - 3

15 u - 7 = 5 u - 3 : u = \frac{2}{5}

15 u - 7 = 5 u - 3

Move

7

to the right side

15 u - 7 = 5 u - 3

Add

7

to both sides

15 u - 7 + 7 = 5 u - 3 + 7

Simplify

15 u = 5 u + 4

15 u = 5 u + 4

Move

5 u

to the left side

15 u = 5 u + 4

Subtract

5 u

from both sides

15 u - 5 u = 5 u + 4 - 5 u

Simplify

10 u = 4

10 u = 4

Divide both sides by

10

10 u = 4

Divide both sides by

10

\frac{10 u}{10} = \frac{4}{10}

Simplify

u = \frac{2}{5}

u = \frac{2}{5}

Substitute back

u = tan (θ)

tan (θ) = \frac{2}{5}

tan (θ) = \frac{2}{5}

tan (θ) = \frac{2}{5} : θ = arctan (\frac{2}{5}) + πn

tan (θ) = \frac{2}{5}

Apply trig inverse properties

tan (θ) = \frac{2}{5}

General solutions for

tan (θ) = \frac{2}{5}

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

θ = arctan (\frac{2}{5}) + πn

θ = arctan (\frac{2}{5}) + πn

Combine all the solutions

θ = arctan (\frac{2}{5}) + πn

Show solutions in decimal form

θ = 0.38050 \dots + πn

Graph

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Frequently Asked Questions (FAQ)

What is the general solution for 15tan(θ)-7=5tan(θ)-3 ?
The general solution for 15tan(θ)-7=5tan(θ)-3 is θ=0.38050…+pin