What is the general solution for 7tan(x)cos(x)=2cos(x) ?

The general solution for 7tan(x)cos(x)=2cos(x) is x=0.27829…+pin

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Popular >

7tan(x)cos(x)=2cos(x)

Solution

7 tan (x) cos (x) = 2 cos (x)

Solution

x = 0.27829 \dots + πn

Degrees

x = 15.94539 \dots^{\circ} + 18 0^{\circ} n

Solution steps

7 tan (x) cos (x) = 2 cos (x)

Subtract

2 cos (x)

from both sides

7 tan (x) cos (x) - 2 cos (x) = 0

Factor

7 tan (x) cos (x) - 2 cos (x) : cos (x) (7 tan (x) - 2)

7 tan (x) cos (x) - 2 cos (x)

Factor out common term

cos (x)

= cos (x) (7 tan (x) - 2)

cos (x) (7 tan (x) - 2) = 0

Solving each part separately

cos (x) = 0 or 7 tan (x) - 2 = 0

cos (x) = 0 : x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

cos (x) = 0

General solutions for

cos (x) = 0

cos (x)

periodicity table with

2 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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

7 tan (x) - 2 = 0 : x = arctan (\frac{2}{7}) + πn

7 tan (x) - 2 = 0

Move

2

to the right side

7 tan (x) - 2 = 0

Add

2

to both sides

7 tan (x) - 2 + 2 = 0 + 2

Simplify

7 tan (x) = 2

7 tan (x) = 2

Divide both sides by

7

7 tan (x) = 2

Divide both sides by

7

\frac{7 tan ( x )}{7} = \frac{2}{7}

Simplify

tan (x) = \frac{2}{7}

tan (x) = \frac{2}{7}

Apply trig inverse properties

tan (x) = \frac{2}{7}

General solutions for

tan (x) = \frac{2}{7}

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

x = arctan (\frac{2}{7}) + πn

x = arctan (\frac{2}{7}) + πn

Combine all the solutions

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn, x = arctan (\frac{2}{7}) + πn

Since the equation is undefined for:

\frac{π}{2} + 2 πn, \frac{3 π}{2} + 2 πn

x = arctan (\frac{2}{7}) + πn

Show solutions in decimal form

x = 0.27829 \dots + πn

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Frequently Asked Questions (FAQ)

What is the general solution for 7tan(x)cos(x)=2cos(x) ?
The general solution for 7tan(x)cos(x)=2cos(x) is x=0.27829…+pin