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Popular >

solvefor t,x=sin(2t)+1

Solution

solve for

t, x = sin (2 t) + 1

Solution

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

Solution steps

x = sin (2 t) + 1

Switch sides

sin (2 t) + 1 = x

Move

1

to the right side

sin (2 t) + 1 = x

Subtract

1

from both sides

sin (2 t) + 1 - 1 = x - 1

Simplify

sin (2 t) = x - 1

sin (2 t) = x - 1

Apply trig inverse properties

sin (2 t) = x - 1

General solutions for

sin (2 t) = x - 1

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

2 t = arcsin (x - 1) + 2 πn, 2 t = π + arcsin (- x + 1) + 2 πn

2 t = arcsin (x - 1) + 2 πn, 2 t = π + arcsin (- x + 1) + 2 πn

Solve

2 t = arcsin (x - 1) + 2 πn : t = \frac{arcsin ( x - 1 )}{2} + πn

2 t = arcsin (x - 1) + 2 πn

Divide both sides by

2

2 t = arcsin (x - 1) + 2 πn

Divide both sides by

2

\frac{2 t}{2} = \frac{arcsin ( x - 1 )}{2} + \frac{2 πn}{2}

Simplify

t = \frac{arcsin ( x - 1 )}{2} + πn

t = \frac{arcsin ( x - 1 )}{2} + πn

Solve

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

2 t = π + arcsin (- x + 1) + 2 πn

Divide both sides by

2

2 t = π + arcsin (- x + 1) + 2 πn

Divide both sides by

2

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

Simplify

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

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

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

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