Sin(2П-t)-cos(3П/2+t)+1=0

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вопрос

To solve the equation sin(2π - t) - cos(3π/2 + t) + 1 = 0, we can use trigonometric identities.

Given:
sin(2π - t) - cos(3π/2 + t) + 1 = 0

We know that sin(2π - t) = sin(2π)cos(t) - cos(2π)sin(t) = 0 - (-1)sin(t) = sin(t) and cos(3π/2 + t) = cos(3π/2)cos(t) + sin(3π/2)sin(t) = 0*cos(t) + (-1)sin(t) = -sin(t).

Therefore, the equation becomes:
sin(t) - (-sin(t)) + 1 = 0
2sin(t) + 1 = 0
2sin(t) = -1
sin(t) = -1/2

Now, we know that sin(t) = -1/2 at t = 7π/6 and t = 11π/6.

So, the solutions to the equation are t = 7π/6 and t = 11π/6.