Solve 3sin(x 1) 2=1

Evaluate

3 sin (x \times 1) \times 2 = 1

Simplify

More Steps

6 sin (x) = 1

Multiply both sides of the equation by \frac{1}{6}

6 sin (x) \times \frac{1}{6} = 1 \times \frac{1}{6}

Calculate

sin (x) = 1 \times \frac{1}{6}

Any expression multiplied by 1 remains the same

sin (x) = \frac{1}{6}

Use the inverse trigonometric function

x = arcsin (\frac{1}{6})

Calculate

x = arcsin (\frac{1}{6}) x = - arcsin (\frac{1}{6}) + π

Add the period of 2 kπ, k \in Z to find all solutions

x = arcsin (\frac{1}{6}) + 2 kπ, k \in Z x = - arcsin (\frac{1}{6}) + π + 2 kπ, k \in Z

Solution

x = {arcsin (\frac{1}{6}) + 2 kπ - arcsin (\frac{1}{6}) + π + 2 kπ, k \in Z

Alternative Form

x \approx {9.59406 8^{\circ} + 36 0^{\circ} k 170.40593 2^{\circ} + 36 0^{\circ} k, k \in Z

Alternative Form

x \approx {0.167448 + 2 kπ 2.974145 + 2 kπ, k \in Z

Solve the equation