What is the general solution for 270=69-tan(45+(x/2)) ?

The general solution for 270=69-tan(45+(x/2)) is x=-2*1.56582…+360n-90

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Popular Trigonometry >

270=69-tan(45+(x/2))

Solution

270 = 69 - tan (4 5^{\circ} + (\frac{x}{2}))

Solution

x = - 2 \cdot 1.56582 \dots + 36 0^{\circ} n - 9 0^{\circ}

Radians

x = - 2 \cdot 1.56582 \dots - \frac{π}{2} + 2 πn

Solution steps

270 = 69 - tan (4 5^{\circ} + (\frac{x}{2}))

Switch sides

69 - tan (4 5^{\circ} + \frac{x}{2}) = 270

Move

69

to the right side

69 - tan (4 5^{\circ} + \frac{x}{2}) = 270

Subtract

69

from both sides

69 - tan (4 5^{\circ} + \frac{x}{2}) - 69 = 270 - 69

Simplify

- tan (4 5^{\circ} + \frac{x}{2}) = 201

- tan (4 5^{\circ} + \frac{x}{2}) = 201

Divide both sides by

- 1

- tan (4 5^{\circ} + \frac{x}{2}) = 201

Divide both sides by

- 1

\frac{- tan ( 4 5 ^{\circ} + \frac{x}{2} )}{- 1} = \frac{201}{- 1}

Simplify

tan (4 5^{\circ} + \frac{x}{2}) = - 201

tan (4 5^{\circ} + \frac{x}{2}) = - 201

Apply trig inverse properties

tan (4 5^{\circ} + \frac{x}{2}) = - 201

General solutions for

tan (4 5^{\circ} + \frac{x}{2}) = - 201

tan (x) = - a \Rightarrow x = arctan (- a) + 18 0^{\circ} n

4 5^{\circ} + \frac{x}{2} = arctan (- 201) + 18 0^{\circ} n

4 5^{\circ} + \frac{x}{2} = arctan (- 201) + 18 0^{\circ} n

Solve

4 5^{\circ} + \frac{x}{2} = arctan (- 201) + 18 0^{\circ} n : x = - 2 arctan (201) + 36 0^{\circ} n - 9 0^{\circ}

4 5^{\circ} + \frac{x}{2} = arctan (- 201) + 18 0^{\circ} n

Simplify

arctan (- 201) + 18 0^{\circ} n : - arctan (201) + 18 0^{\circ} n

arctan (- 201) + 18 0^{\circ} n

Use the following property:

arctan (- x) = - arctan (x)

arctan (- 201) = - arctan (201)

= - arctan (201) + 18 0^{\circ} n

4 5^{\circ} + \frac{x}{2} = - arctan (201) + 18 0^{\circ} n

Move

4 5^{\circ}

to the right side

4 5^{\circ} + \frac{x}{2} = - arctan (201) + 18 0^{\circ} n

Subtract

4 5^{\circ}

from both sides

4 5^{\circ} + \frac{x}{2} - 4 5^{\circ} = - arctan (201) + 18 0^{\circ} n - 4 5^{\circ}

Simplify

\frac{x}{2} = - arctan (201) + 18 0^{\circ} n - 4 5^{\circ}

\frac{x}{2} = - arctan (201) + 18 0^{\circ} n - 4 5^{\circ}

Multiply both sides by

2

\frac{x}{2} = - arctan (201) + 18 0^{\circ} n - 4 5^{\circ}

Multiply both sides by

2

\frac{2 x}{2} = - 2 arctan (201) + 36 0^{\circ} n - 2 \cdot 4 5^{\circ}

Simplify

\frac{2 x}{2} = - 2 arctan (201) + 36 0^{\circ} n - 2 \cdot 4 5^{\circ}

Simplify

\frac{2 x}{2} : x

\frac{2 x}{2}

Divide the numbers:

\frac{2}{2} = 1

= x

Simplify

- 2 arctan (201) + 36 0^{\circ} n - 2 \cdot 4 5^{\circ} : - 2 arctan (201) + 36 0^{\circ} n - 9 0^{\circ}

- 2 arctan (201) + 36 0^{\circ} n - 2 \cdot 4 5^{\circ}

2 \cdot 4 5^{\circ} = 9 0^{\circ}

2 \cdot 4 5^{\circ}

Multiply fractions:

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

= 9 0^{\circ}

Cancel the common factor:

2

= 9 0^{\circ}

= - 2 arctan (201) + 36 0^{\circ} n - 9 0^{\circ}

x = - 2 arctan (201) + 36 0^{\circ} n - 9 0^{\circ}

x = - 2 arctan (201) + 36 0^{\circ} n - 9 0^{\circ}

x = - 2 arctan (201) + 36 0^{\circ} n - 9 0^{\circ}

x = - 2 arctan (201) + 36 0^{\circ} n - 9 0^{\circ}

Show solutions in decimal form

x = - 2 \cdot 1.56582 \dots + 36 0^{\circ} n - 9 0^{\circ}

Graph

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Frequently Asked Questions (FAQ)

What is the general solution for 270=69-tan(45+(x/2)) ?
The general solution for 270=69-tan(45+(x/2)) is x=-2*1.56582…+360n-90