What is the general solution for tan(6.5^2-a)=8 ?

The general solution for tan(6.5^2-a)=8 is a=42.25-pin-1.44644…

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Popular >

tan(6.5^2-a)=8

Solution

tan (6. 5^{2} - a) = 8

Solution

a = 42.25 - πn - 1.44644 \dots

Degrees

a = 2337.87170 \dots^{\circ} - 18 0^{\circ} n

Solution steps

tan (6. 5^{2} - a) = 8

Apply trig inverse properties

tan (6. 5^{2} - a) = 8

General solutions for

tan (6. 5^{2} - a) = 8

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

6. 5^{2} - a = arctan (8) + πn

6. 5^{2} - a = arctan (8) + πn

Solve

6. 5^{2} - a = arctan (8) + πn : a = 42.25 - πn - arctan (8)

6. 5^{2} - a = arctan (8) + πn

6. 5^{2} = 42.25

42.25 - a = arctan (8) + πn

Move

42.25

to the right side

42.25 - a = arctan (8) + πn

Subtract

42.25

from both sides

42.25 - a - 42.25 = arctan (8) + πn - 42.25

Simplify

- a = arctan (8) + πn - 42.25

- a = arctan (8) + πn - 42.25

Divide both sides by

- 1

- a = arctan (8) + πn - 42.25

Divide both sides by

- 1

\frac{- a}{- 1} = \frac{arctan ( 8 )}{- 1} + \frac{πn}{- 1} - \frac{42.25}{- 1}

Simplify

\frac{- a}{- 1} = \frac{arctan ( 8 )}{- 1} + \frac{πn}{- 1} - \frac{42.25}{- 1}

Simplify

\frac{- a}{- 1} : a

\frac{- a}{- 1}

Apply the fraction rule:

\frac{- a}{- b} = \frac{a}{b}

= \frac{a}{1}

Apply rule

\frac{a}{1} = a

= a

Simplify

\frac{arctan ( 8 )}{- 1} + \frac{πn}{- 1} - \frac{42.25}{- 1} : 42.25 - πn - arctan (8)

\frac{arctan ( 8 )}{- 1} + \frac{πn}{- 1} - \frac{42.25}{- 1}

Group like terms

= - \frac{42.25}{- 1} + \frac{πn}{- 1} + \frac{arctan ( 8 )}{- 1}

\frac{42.25}{- 1} = - 42.25

\frac{42.25}{- 1}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{42.25}{1}

Apply rule

\frac{a}{1} = a

= - 42.25

\frac{πn}{- 1} = - πn

\frac{πn}{- 1}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{πn}{1}

Apply rule

\frac{a}{1} = a

= - πn

= - (- 42.25) - πn + \frac{arctan ( 8 )}{- 1}

Apply rule

- (- a) = a

= 42.25 - πn + \frac{arctan ( 8 )}{- 1}

\frac{arctan ( 8 )}{- 1} = - arctan (8)

\frac{arctan ( 8 )}{- 1}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{arctan ( 8 )}{1}

Apply rule

\frac{a}{1} = a

= - arctan (8)

= 42.25 - πn - arctan (8)

a = 42.25 - πn - arctan (8)

a = 42.25 - πn - arctan (8)

a = 42.25 - πn - arctan (8)

a = 42.25 - πn - arctan (8)

Show solutions in decimal form

a = 42.25 - πn - 1.44644 \dots

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Frequently Asked Questions (FAQ)

What is the general solution for tan(6.5^2-a)=8 ?
The general solution for tan(6.5^2-a)=8 is a=42.25-pin-1.44644…