What is the general solution for 6=10cos(4*o) ?

The general solution for 6=10cos(4*o) is o=(0.92729…)/4+(pin)/2 ,o= pi/2-(0.92729…)/4+(pin)/2

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Popular Trigonometry >

6=10cos(4*o)

Solution

6 = 10 cos (4 \cdot o)

Solution

o = \frac{0.92729 \dots}{4} + \frac{πn}{2}, o = \frac{π}{2} - \frac{0.92729 \dots}{4} + \frac{πn}{2}

Degrees

o = 13.28252 \dots^{\circ} + 9 0^{\circ} n, o = 76.71747 \dots^{\circ} + 9 0^{\circ} n

Solution steps

6 = 10 cos (4 o)

Switch sides

10 cos (4 o) = 6

Divide both sides by

10

10 cos (4 o) = 6

Divide both sides by

10

\frac{10 cos ( 4 o )}{10} = \frac{6}{10}

Simplify

cos (4 o) = \frac{3}{5}

cos (4 o) = \frac{3}{5}

Apply trig inverse properties

cos (4 o) = \frac{3}{5}

General solutions for

cos (4 o) = \frac{3}{5}

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

4 o = arccos (\frac{3}{5}) + 2 πn, 4 o = 2 π - arccos (\frac{3}{5}) + 2 πn

4 o = arccos (\frac{3}{5}) + 2 πn, 4 o = 2 π - arccos (\frac{3}{5}) + 2 πn

Solve

4 o = arccos (\frac{3}{5}) + 2 πn : o = \frac{arccos ( \frac{3}{5} )}{4} + \frac{πn}{2}

4 o = arccos (\frac{3}{5}) + 2 πn

Divide both sides by

4

4 o = arccos (\frac{3}{5}) + 2 πn

Divide both sides by

4

\frac{4 o}{4} = \frac{arccos ( \frac{3}{5} )}{4} + \frac{2 πn}{4}

Simplify

o = \frac{arccos ( \frac{3}{5} )}{4} + \frac{πn}{2}

o = \frac{arccos ( \frac{3}{5} )}{4} + \frac{πn}{2}

Solve

4 o = 2 π - arccos (\frac{3}{5}) + 2 πn : o = \frac{π}{2} - \frac{arccos ( \frac{3}{5} )}{4} + \frac{πn}{2}

4 o = 2 π - arccos (\frac{3}{5}) + 2 πn

Divide both sides by

4

4 o = 2 π - arccos (\frac{3}{5}) + 2 πn

Divide both sides by

4

\frac{4 o}{4} = \frac{2 π}{4} - \frac{arccos ( \frac{3}{5} )}{4} + \frac{2 πn}{4}

Simplify

\frac{4 o}{4} = \frac{2 π}{4} - \frac{arccos ( \frac{3}{5} )}{4} + \frac{2 πn}{4}

Simplify

\frac{4 o}{4} : o

\frac{4 o}{4}

Divide the numbers:

\frac{4}{4} = 1

= o

Simplify

\frac{2 π}{4} - \frac{arccos ( \frac{3}{5} )}{4} + \frac{2 πn}{4} : \frac{π}{2} - \frac{arccos ( \frac{3}{5} )}{4} + \frac{πn}{2}

\frac{2 π}{4} - \frac{arccos ( \frac{3}{5} )}{4} + \frac{2 πn}{4}

Cancel

\frac{2 π}{4} : \frac{π}{2}

\frac{2 π}{4}

Cancel the common factor:

2

= \frac{π}{2}

= \frac{π}{2} - \frac{arccos ( \frac{3}{5} )}{4} + \frac{2 πn}{4}

Cancel

\frac{2 πn}{4} : \frac{πn}{2}

\frac{2 πn}{4}

Cancel the common factor:

2

= \frac{πn}{2}

= \frac{π}{2} - \frac{arccos ( \frac{3}{5} )}{4} + \frac{πn}{2}

o = \frac{π}{2} - \frac{arccos ( \frac{3}{5} )}{4} + \frac{πn}{2}

o = \frac{π}{2} - \frac{arccos ( \frac{3}{5} )}{4} + \frac{πn}{2}

o = \frac{π}{2} - \frac{arccos ( \frac{3}{5} )}{4} + \frac{πn}{2}

o = \frac{arccos ( \frac{3}{5} )}{4} + \frac{πn}{2}, o = \frac{π}{2} - \frac{arccos ( \frac{3}{5} )}{4} + \frac{πn}{2}

Show solutions in decimal form

o = \frac{0.92729 \dots}{4} + \frac{πn}{2}, o = \frac{π}{2} - \frac{0.92729 \dots}{4} + \frac{πn}{2}

Graph

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Frequently Asked Questions (FAQ)

What is the general solution for 6=10cos(4*o) ?
The general solution for 6=10cos(4*o) is o=(0.92729…)/4+(pin)/2 ,o= pi/2-(0.92729…)/4+(pin)/2