en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sin(2t-pi/5)=-1/3

Solution

sin (2 t - \frac{π}{5}) = - \frac{1}{3}

Solution

t = πn + \frac{π}{10} - \frac{0.33983 \dots}{2}, t = πn + \frac{π}{2} + \frac{π}{10} + \frac{0.33983 \dots}{2}

+1

Degrees

t = 8.26438 \dots^{\circ} + 18 0^{\circ} n, t = 117.73561 \dots^{\circ} + 18 0^{\circ} n

Solution steps

sin (2 t - \frac{π}{5}) = - \frac{1}{3}

Apply trig inverse properties

sin (2 t - \frac{π}{5}) = - \frac{1}{3}

General solutions for

sin (2 t - \frac{π}{5}) = - \frac{1}{3}

sin (x) = - a \Rightarrow x = arcsin (- a) + 2 πn, x = π + arcsin (a) + 2 πn

2 t - \frac{π}{5} = arcsin (- \frac{1}{3}) + 2 πn, 2 t - \frac{π}{5} = π + arcsin (\frac{1}{3}) + 2 πn

2 t - \frac{π}{5} = arcsin (- \frac{1}{3}) + 2 πn, 2 t - \frac{π}{5} = π + arcsin (\frac{1}{3}) + 2 πn

Solve

2 t - \frac{π}{5} = arcsin (- \frac{1}{3}) + 2 πn : t = πn + \frac{π}{10} - \frac{arcsin ( \frac{1}{3} )}{2}

2 t - \frac{π}{5} = arcsin (- \frac{1}{3}) + 2 πn

Simplify

arcsin (- \frac{1}{3}) + 2 πn : - arcsin (\frac{1}{3}) + 2 πn

arcsin (- \frac{1}{3}) + 2 πn

Use the following property:

arcsin (- x) = - arcsin (x)

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

= - arcsin (\frac{1}{3}) + 2 πn

2 t - \frac{π}{5} = - arcsin (\frac{1}{3}) + 2 πn

Move

\frac{π}{5}

to the right side

2 t - \frac{π}{5} = - arcsin (\frac{1}{3}) + 2 πn

Add

\frac{π}{5}

to both sides

2 t - \frac{π}{5} + \frac{π}{5} = - arcsin (\frac{1}{3}) + 2 πn + \frac{π}{5}

Simplify

2 t = - arcsin (\frac{1}{3}) + 2 πn + \frac{π}{5}

2 t = - arcsin (\frac{1}{3}) + 2 πn + \frac{π}{5}

Divide both sides by

2

2 t = - arcsin (\frac{1}{3}) + 2 πn + \frac{π}{5}

Divide both sides by

2

\frac{2 t}{2} = - \frac{arcsin ( \frac{1}{3} )}{2} + \frac{2 πn}{2} + \frac{\frac{π}{5}}{2}

Simplify

\frac{2 t}{2} = - \frac{arcsin ( \frac{1}{3} )}{2} + \frac{2 πn}{2} + \frac{\frac{π}{5}}{2}

Simplify

\frac{2 t}{2} : t

\frac{2 t}{2}

Divide the numbers:

\frac{2}{2} = 1

= t

Simplify

- \frac{arcsin ( \frac{1}{3} )}{2} + \frac{2 πn}{2} + \frac{\frac{π}{5}}{2} : πn + \frac{π}{10} - \frac{arcsin ( \frac{1}{3} )}{2}

- \frac{arcsin ( \frac{1}{3} )}{2} + \frac{2 πn}{2} + \frac{\frac{π}{5}}{2}

Group like terms

= \frac{2 πn}{2} + \frac{\frac{π}{5}}{2} - \frac{arcsin ( \frac{1}{3} )}{2}

\frac{2 πn}{2} = πn

\frac{2 πn}{2}

Divide the numbers:

\frac{2}{2} = 1

= πn

\frac{\frac{π}{5}}{2} = \frac{π}{10}

\frac{\frac{π}{5}}{2}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{π}{5 \cdot 2}

Multiply the numbers:

5 \cdot 2 = 10

= \frac{π}{10}

= πn + \frac{π}{10} - \frac{arcsin ( \frac{1}{3} )}{2}

t = πn + \frac{π}{10} - \frac{arcsin ( \frac{1}{3} )}{2}

t = πn + \frac{π}{10} - \frac{arcsin ( \frac{1}{3} )}{2}

t = πn + \frac{π}{10} - \frac{arcsin ( \frac{1}{3} )}{2}

Solve

2 t - \frac{π}{5} = π + arcsin (\frac{1}{3}) + 2 πn : t = πn + \frac{π}{2} + \frac{π}{10} + \frac{arcsin ( \frac{1}{3} )}{2}

2 t - \frac{π}{5} = π + arcsin (\frac{1}{3}) + 2 πn

Move

\frac{π}{5}

to the right side

2 t - \frac{π}{5} = π + arcsin (\frac{1}{3}) + 2 πn

Add

\frac{π}{5}

to both sides

2 t - \frac{π}{5} + \frac{π}{5} = π + arcsin (\frac{1}{3}) + 2 πn + \frac{π}{5}

Simplify

2 t = π + arcsin (\frac{1}{3}) + 2 πn + \frac{π}{5}

2 t = π + arcsin (\frac{1}{3}) + 2 πn + \frac{π}{5}

Divide both sides by

2

2 t = π + arcsin (\frac{1}{3}) + 2 πn + \frac{π}{5}

Divide both sides by

2

\frac{2 t}{2} = \frac{π}{2} + \frac{arcsin ( \frac{1}{3} )}{2} + \frac{2 πn}{2} + \frac{\frac{π}{5}}{2}

Simplify

\frac{2 t}{2} = \frac{π}{2} + \frac{arcsin ( \frac{1}{3} )}{2} + \frac{2 πn}{2} + \frac{\frac{π}{5}}{2}

Simplify

\frac{2 t}{2} : t

\frac{2 t}{2}

Divide the numbers:

\frac{2}{2} = 1

= t

Simplify

\frac{π}{2} + \frac{arcsin ( \frac{1}{3} )}{2} + \frac{2 πn}{2} + \frac{\frac{π}{5}}{2} : πn + \frac{π}{2} + \frac{π}{10} + \frac{arcsin ( \frac{1}{3} )}{2}

\frac{π}{2} + \frac{arcsin ( \frac{1}{3} )}{2} + \frac{2 πn}{2} + \frac{\frac{π}{5}}{2}

Group like terms

= \frac{π}{2} + \frac{2 πn}{2} + \frac{\frac{π}{5}}{2} + \frac{arcsin ( \frac{1}{3} )}{2}

\frac{2 πn}{2} = πn

\frac{2 πn}{2}

Divide the numbers:

\frac{2}{2} = 1

= πn

\frac{\frac{π}{5}}{2} = \frac{π}{10}

\frac{\frac{π}{5}}{2}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{π}{5 \cdot 2}

Multiply the numbers:

5 \cdot 2 = 10

= \frac{π}{10}

= \frac{π}{2} + πn + \frac{π}{10} + \frac{arcsin ( \frac{1}{3} )}{2}

Group like terms

= πn + \frac{π}{2} + \frac{π}{10} + \frac{arcsin ( \frac{1}{3} )}{2}

t = πn + \frac{π}{2} + \frac{π}{10} + \frac{arcsin ( \frac{1}{3} )}{2}

t = πn + \frac{π}{2} + \frac{π}{10} + \frac{arcsin ( \frac{1}{3} )}{2}

t = πn + \frac{π}{2} + \frac{π}{10} + \frac{arcsin ( \frac{1}{3} )}{2}

t = πn + \frac{π}{10} - \frac{arcsin ( \frac{1}{3} )}{2}, t = πn + \frac{π}{2} + \frac{π}{10} + \frac{arcsin ( \frac{1}{3} )}{2}

Show solutions in decimal form

t = πn + \frac{π}{10} - \frac{0.33983 \dots}{2}, t = πn + \frac{π}{2} + \frac{π}{10} + \frac{0.33983 \dots}{2}

Popular Examples

2(sin(x))^2-cos(x)-1=0

2 (sin (x))^{2} - cos (x) - 1 = 0

arctan(3x)+arctan(x)= pi/4

arctan (3 x) + arctan (x) = \frac{π}{4}

4sin(θ)=sqrt(3)sec(θ),0<= θ<180

4 sin (θ) = 3 sec (θ), 0 \leq θ < 18 0^{\circ}

(sin(82))/(sin(x))=sqrt(5)

\frac{sin ( 8 2 ^{\circ} )}{sin ( x )} = 5

(2cos^2(x))/(2(1-sin(x))-cos^2(x))=0

\frac{2 cos ^{2} ( x )}{2 ( 1 - sin ( x ) ) - cos ^{2} ( x )} = 0