What is the general solution for solvefor y,3tan(y)-4= 2/5 ?

The general solution for solvefor y,3tan(y)-4= 2/5 is y=0.97237…+pin

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Popular >

solvefor y,3tan(y)-4= 2/5

Solution

solve for

y, 3 tan (y) - 4 = \frac{2}{5}

Solution

y = 0.97237 \dots + πn

Degrees

y = 55.71312 \dots^{\circ} + 18 0^{\circ} n

Solution steps

3 tan (y) - 4 = \frac{2}{5}

Move

4

to the right side

3 tan (y) - 4 = \frac{2}{5}

Add

4

to both sides

3 tan (y) - 4 + 4 = \frac{2}{5} + 4

Simplify

3 tan (y) - 4 + 4 = \frac{2}{5} + 4

Simplify

3 tan (y) - 4 + 4 : 3 tan (y)

3 tan (y) - 4 + 4

Add similar elements:

- 4 + 4 = 0

= 3 tan (y)

Simplify

\frac{2}{5} + 4 : \frac{22}{5}

\frac{2}{5} + 4

Convert element to fraction:

4 = \frac{4 \cdot 5}{5}

= \frac{4 \cdot 5}{5} + \frac{2}{5}

Since the denominators are equal, combine the fractions:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{4 \cdot 5 + 2}{5}

4 \cdot 5 + 2 = 22

4 \cdot 5 + 2

Multiply the numbers:

4 \cdot 5 = 20

= 20 + 2

Add the numbers:

20 + 2 = 22

= 22

= \frac{22}{5}

3 tan (y) = \frac{22}{5}

3 tan (y) = \frac{22}{5}

3 tan (y) = \frac{22}{5}

Divide both sides by

3

3 tan (y) = \frac{22}{5}

Divide both sides by

3

\frac{3 tan ( y )}{3} = \frac{\frac{22}{5}}{3}

Simplify

\frac{3 tan ( y )}{3} = \frac{\frac{22}{5}}{3}

Simplify

\frac{3 tan ( y )}{3} : tan (y)

\frac{3 tan ( y )}{3}

Divide the numbers:

\frac{3}{3} = 1

= tan (y)

Simplify

\frac{\frac{22}{5}}{3} : \frac{22}{15}

\frac{\frac{22}{5}}{3}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{22}{5 \cdot 3}

Multiply the numbers:

5 \cdot 3 = 15

= \frac{22}{15}

tan (y) = \frac{22}{15}

tan (y) = \frac{22}{15}

tan (y) = \frac{22}{15}

Apply trig inverse properties

tan (y) = \frac{22}{15}

General solutions for

tan (y) = \frac{22}{15}

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

y = arctan (\frac{22}{15}) + πn

y = arctan (\frac{22}{15}) + πn

Show solutions in decimal form

y = 0.97237 \dots + πn

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Frequently Asked Questions (FAQ)

What is the general solution for solvefor y,3tan(y)-4= 2/5 ?
The general solution for solvefor y,3tan(y)-4= 2/5 is y=0.97237…+pin