solvefor t,y=-y+sin(t)+cos(t)

Solution

solve for

t, y = - y + sin (t) + cos (t)

t = arcsin (2 y) + 2 πn - \frac{π}{4}, t = π + arcsin (- 2 y) + 2 πn - \frac{π}{4}

Solution steps

y = - y + sin (t) + cos (t)

Switch sides

- y + sin (t) + cos (t) = y

Rewrite using trig identities

- y + 2 sin (t + \frac{π}{4}) = y

Move

y

to the right side

2 sin (t + \frac{π}{4}) = 2 y

Divide both sides by

2

sin (t + \frac{π}{4}) = 2 y

Apply trig inverse properties

t + \frac{π}{4} = arcsin (2 y) + 2 πn, t + \frac{π}{4} = π + arcsin (- 2 y) + 2 πn

Solve

t + \frac{π}{4} = arcsin (2 y) + 2 πn : t = arcsin (2 y) + 2 πn - \frac{π}{4}

Solve

t + \frac{π}{4} = π + arcsin (- 2 y) + 2 πn : t = π + arcsin (- 2 y) + 2 πn - \frac{π}{4}

t = arcsin (2 y) + 2 πn - \frac{π}{4}, t = π + arcsin (- 2 y) + 2 πn - \frac{π}{4}

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

sin (x) = \frac{- \frac{4}{3} 3}{\frac{8}{3} 3}

sec (a) = \frac{5}{4}

cot^{4} (x) - 9 = 0

0.5 \cdot sin (x) = 1 \cdot (645 \cdot 1 0^{- 9})