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# Basic Trigonometric Ratios

### Finding all the angles between $$0^\circ$$ and $$360^\circ$$

Using the fact that each ratio is positive (or negative) in two quadrants, if you are asked to find the angle you expect to have two answers.

For example: Find $$\theta$$ between $$0^{\circ}\leq \theta < 360^\circ$$ such that $$\sin\theta=0.3$$.

This example has two solutions as $$\sin$$ is positive in two quadrants, the first quadrant and the second quadrant.

Calculator gives: $\theta=\sin^{-1} 0.3\approx 17.46^{\circ}$

To get the angle in the second quadrant: $\theta =180^{\circ}-17.46^{\circ}=162.54^{\circ}$

The two solutions can be seen in the below figure: