What is the general solution for -(2)cos(10t)=(6)sin(10t) ?

The general solution for -(2)cos(10t)=(6)sin(10t) is t=-(0.32175…)/(10)+(pin)/(10)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

-(2)cos(10t)=(6)sin(10t)

Solution

- (2) cos (10 t) = (6) sin (10 t)

Solution

t = - \frac{0.32175 \dots}{10} + \frac{πn}{10}

Degrees

t = - 1.84349 \dots^{\circ} + 1 8^{\circ} n

Solution steps

- (2) cos (10 t) = (6) sin (10 t)

Rewrite using trig identities

- 2 cos (10 t) = 6 sin (10 t)

Divide both sides by

cos (10 t), cos (10 t) \neq = 0

\frac{- 2 cos ( 10 t )}{cos ( 10 t )} = \frac{6 sin ( 10 t )}{cos ( 10 t )}

Simplify

- 2 = \frac{6 sin ( 10 t )}{cos ( 10 t )}

Use the basic trigonometric identity:

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

- 2 = 6 tan (10 t)

Switch sides

6 tan (10 t) = - 2

6 tan (10 t) = - 2

Divide both sides by

6

6 tan (10 t) = - 2

Divide both sides by

6

\frac{6 tan ( 10 t )}{6} = \frac{- 2}{6}

Simplify

\frac{6 tan ( 10 t )}{6} = \frac{- 2}{6}

Simplify

\frac{6 tan ( 10 t )}{6} : tan (10 t)

\frac{6 tan ( 10 t )}{6}

Divide the numbers:

\frac{6}{6} = 1

= tan (10 t)

Simplify

\frac{- 2}{6} : - \frac{1}{3}

\frac{- 2}{6}

Apply the fraction rule:

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

= - \frac{2}{6}

Cancel the common factor:

2

= - \frac{1}{3}

tan (10 t) = - \frac{1}{3}

tan (10 t) = - \frac{1}{3}

tan (10 t) = - \frac{1}{3}

Apply trig inverse properties

tan (10 t) = - \frac{1}{3}

General solutions for

tan (10 t) = - \frac{1}{3}

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

10 t = arctan (- \frac{1}{3}) + πn

10 t = arctan (- \frac{1}{3}) + πn

Solve

10 t = arctan (- \frac{1}{3}) + πn : t = - \frac{arctan ( \frac{1}{3} )}{10} + \frac{πn}{10}

10 t = arctan (- \frac{1}{3}) + πn

Simplify

arctan (- \frac{1}{3}) + πn : - arctan (\frac{1}{3}) + πn

arctan (- \frac{1}{3}) + πn

Use the following property:

arctan (- x) = - arctan (x)

arctan (- \frac{1}{3}) = - arctan (\frac{1}{3})

= - arctan (\frac{1}{3}) + πn

10 t = - arctan (\frac{1}{3}) + πn

Divide both sides by

10

10 t = - arctan (\frac{1}{3}) + πn

Divide both sides by

10

\frac{10 t}{10} = - \frac{arctan ( \frac{1}{3} )}{10} + \frac{πn}{10}

Simplify

t = - \frac{arctan ( \frac{1}{3} )}{10} + \frac{πn}{10}

t = - \frac{arctan ( \frac{1}{3} )}{10} + \frac{πn}{10}

t = - \frac{arctan ( \frac{1}{3} )}{10} + \frac{πn}{10}

Show solutions in decimal form

t = - \frac{0.32175 \dots}{10} + \frac{πn}{10}

Popular Examples

cot(x)= 1/4

cot (x) = \frac{1}{4}

tan(x)=0,0<x<2pi

tan (x) = 0, 0 < x < 2 π

solvefor x,sin(x)+cos(y)=2y solve for

x, sin (x) + cos (y) = 2 y

4sin(b)+sqrt(8)=0

4 sin (b) + 8 = 0

sin(x)= 73/83

sin (x) = \frac{73}{83}

Frequently Asked Questions (FAQ)

What is the general solution for -(2)cos(10t)=(6)sin(10t) ?
The general solution for -(2)cos(10t)=(6)sin(10t) is t=-(0.32175…)/(10)+(pin)/(10)