Year 10: Radians and degrees

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In Australian Year 10 Mathematics, angles can be measured in degrees or radians. Degrees are more familiar, but radians are essential once trigonometry becomes more advanced. The key idea is that both units measure the same turning amount.

Work through the sections in order, then try the linked Year 10 skill quizzes after each section.

From degrees to radians

To convert degrees into radians, multiply the degree value by $\pi /180$. Leave answers in exact form when possible.

From radians to degrees

To convert radians into degrees, multiply by $180/\pi$.

Common exact angles

Some conversions appear so often that it is worth memorising them: $30°=\pi /6$, $45°=\pi /4$, $90°=\pi /2$, and $360°=2\pi$.

Common mistakes

• Using the wrong fraction and converting the value in the wrong direction.
• Turning an exact radian answer into a decimal too early.
• Forgetting that the $\pi$ should usually stay in the exact final answer.

Study routine

Start by writing $180°=\pi$ at the top of the page. Then decide whether you need $\pi /180$ or $180/\pi$. That keeps the method consistent.