What is the general solution for 8cos(2t)-14sin(2t)=0 ?

The general solution for 8cos(2t)-14sin(2t)=0 is t=(0.51914…)/2+(pin)/2

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Popular >

8cos(2t)-14sin(2t)=0

Solution

8 cos (2 t) - 14 sin (2 t) = 0

Solution

t = \frac{0.51914 \dots}{2} + \frac{πn}{2}

Degrees

t = 14.87244 \dots^{\circ} + 9 0^{\circ} n

Solution steps

8 cos (2 t) - 14 sin (2 t) = 0

Rewrite using trig identities

8 cos (2 t) - 14 sin (2 t) = 0

Divide both sides by

cos (2 t), cos (2 t) \neq = 0

\frac{8 cos ( 2 t ) - 14 sin ( 2 t )}{cos ( 2 t )} = \frac{0}{cos ( 2 t )}

Simplify

8 - \frac{14 sin ( 2 t )}{cos ( 2 t )} = 0

Use the basic trigonometric identity:

\frac{sin ( x )}{cos ( x )} = tan (x)

8 - 14 tan (2 t) = 0

8 - 14 tan (2 t) = 0

Move

8

to the right side

8 - 14 tan (2 t) = 0

Subtract

8

from both sides

8 - 14 tan (2 t) - 8 = 0 - 8

Simplify

- 14 tan (2 t) = - 8

- 14 tan (2 t) = - 8

Divide both sides by

- 14

- 14 tan (2 t) = - 8

Divide both sides by

- 14

\frac{- 14 tan ( 2 t )}{- 14} = \frac{- 8}{- 14}

Simplify

\frac{- 14 tan ( 2 t )}{- 14} = \frac{- 8}{- 14}

Simplify

\frac{- 14 tan ( 2 t )}{- 14} : tan (2 t)

\frac{- 14 tan ( 2 t )}{- 14}

Apply the fraction rule:

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

= \frac{14 tan ( 2 t )}{14}

Divide the numbers:

\frac{14}{14} = 1

= tan (2 t)

Simplify

\frac{- 8}{- 14} : \frac{4}{7}

\frac{- 8}{- 14}

Apply the fraction rule:

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

= \frac{8}{14}

Cancel the common factor:

2

= \frac{4}{7}

tan (2 t) = \frac{4}{7}

tan (2 t) = \frac{4}{7}

tan (2 t) = \frac{4}{7}

Apply trig inverse properties

tan (2 t) = \frac{4}{7}

General solutions for

tan (2 t) = \frac{4}{7}

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

2 t = arctan (\frac{4}{7}) + πn

2 t = arctan (\frac{4}{7}) + πn

Solve

2 t = arctan (\frac{4}{7}) + πn : t = \frac{arctan ( \frac{4}{7} )}{2} + \frac{πn}{2}

2 t = arctan (\frac{4}{7}) + πn

Divide both sides by

2

2 t = arctan (\frac{4}{7}) + πn

Divide both sides by

2

\frac{2 t}{2} = \frac{arctan ( \frac{4}{7} )}{2} + \frac{πn}{2}

Simplify

t = \frac{arctan ( \frac{4}{7} )}{2} + \frac{πn}{2}

t = \frac{arctan ( \frac{4}{7} )}{2} + \frac{πn}{2}

t = \frac{arctan ( \frac{4}{7} )}{2} + \frac{πn}{2}

Show solutions in decimal form

t = \frac{0.51914 \dots}{2} + \frac{πn}{2}

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Frequently Asked Questions (FAQ)

What is the general solution for 8cos(2t)-14sin(2t)=0 ?
The general solution for 8cos(2t)-14sin(2t)=0 is t=(0.51914…)/2+(pin)/2