What is the general solution for 9cos(x)tan(x)=-8tan(x) ?

The general solution for 9cos(x)tan(x)=-8tan(x) is x=pin,x=2.66571…+2pin,x=-2.66571…+2pin

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Popular >

9cos(x)tan(x)=-8tan(x)

Solution

9 cos (x) tan (x) = - 8 tan (x)

Solution

x = πn, x = 2.66571 \dots + 2 πn, x = - 2.66571 \dots + 2 πn

Degrees

x = 0^{\circ} + 18 0^{\circ} n, x = 152.73395 \dots^{\circ} + 36 0^{\circ} n, x = - 152.73395 \dots^{\circ} + 36 0^{\circ} n

Solution steps

9 cos (x) tan (x) = - 8 tan (x)

Subtract

- 8 tan (x)

from both sides

9 cos (x) tan (x) + 8 tan (x) = 0

Factor

9 cos (x) tan (x) + 8 tan (x) : tan (x) (9 cos (x) + 8)

9 cos (x) tan (x) + 8 tan (x)

Factor out common term

tan (x)

= tan (x) (9 cos (x) + 8)

tan (x) (9 cos (x) + 8) = 0

Solving each part separately

tan (x) = 0 or 9 cos (x) + 8 = 0

tan (x) = 0 : x = πn

tan (x) = 0

General solutions for

tan (x) = 0

tan (x)

periodicity table with

πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

x = 0 + πn

x = 0 + πn

Solve

x = 0 + πn : x = πn

x = 0 + πn

0 + πn = πn

x = πn

x = πn

9 cos (x) + 8 = 0 : x = arccos (- \frac{8}{9}) + 2 πn, x = - arccos (- \frac{8}{9}) + 2 πn

9 cos (x) + 8 = 0

Move

8

to the right side

9 cos (x) + 8 = 0

Subtract

8

from both sides

9 cos (x) + 8 - 8 = 0 - 8

Simplify

9 cos (x) = - 8

9 cos (x) = - 8

Divide both sides by

9

9 cos (x) = - 8

Divide both sides by

9

\frac{9 cos ( x )}{9} = \frac{- 8}{9}

Simplify

cos (x) = - \frac{8}{9}

cos (x) = - \frac{8}{9}

Apply trig inverse properties

cos (x) = - \frac{8}{9}

General solutions for

cos (x) = - \frac{8}{9}

cos (x) = - a \Rightarrow x = arccos (- a) + 2 πn, x = - arccos (- a) + 2 πn

x = arccos (- \frac{8}{9}) + 2 πn, x = - arccos (- \frac{8}{9}) + 2 πn

x = arccos (- \frac{8}{9}) + 2 πn, x = - arccos (- \frac{8}{9}) + 2 πn

Combine all the solutions

x = πn, x = arccos (- \frac{8}{9}) + 2 πn, x = - arccos (- \frac{8}{9}) + 2 πn

Show solutions in decimal form

x = πn, x = 2.66571 \dots + 2 πn, x = - 2.66571 \dots + 2 πn

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Frequently Asked Questions (FAQ)

What is the general solution for 9cos(x)tan(x)=-8tan(x) ?
The general solution for 9cos(x)tan(x)=-8tan(x) is x=pin,x=2.66571…+2pin,x=-2.66571…+2pin