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Popular >

solvefor t,3cos(5t)=2

Solution

solve for

t, 3 cos (5 t) = 2

Solution

t = \frac{0.84106 \dots}{5} + \frac{2 πn}{5}, t = \frac{2 π}{5} - \frac{0.84106 \dots}{5} + \frac{2 πn}{5}

+1

Degrees

t = 9.63793 \dots^{\circ} + 7 2^{\circ} n, t = 62.36206 \dots^{\circ} + 7 2^{\circ} n

Solution steps

3 cos (5 t) = 2

Divide both sides by

3

3 cos (5 t) = 2

Divide both sides by

3

\frac{3 cos ( 5 t )}{3} = \frac{2}{3}

Simplify

cos (5 t) = \frac{2}{3}

cos (5 t) = \frac{2}{3}

Apply trig inverse properties

cos (5 t) = \frac{2}{3}

General solutions for

cos (5 t) = \frac{2}{3}

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

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

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

Solve

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

5 t = arccos (\frac{2}{3}) + 2 πn

Divide both sides by

5

5 t = arccos (\frac{2}{3}) + 2 πn

Divide both sides by

5

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

Simplify

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

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

Solve

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

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

Divide both sides by

5

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

Divide both sides by

5

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

Simplify

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

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

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

Show solutions in decimal form

t = \frac{0.84106 \dots}{5} + \frac{2 πn}{5}, t = \frac{2 π}{5} - \frac{0.84106 \dots}{5} + \frac{2 πn}{5}

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