Trigonometry

Learn how to measure angles in degrees (as a fraction of a full turn) and in radians (where $\pi$ radians equals $180°$), and practise converting between the two systems.

Learn how to label the sides of a right-angled triangle (hypotenuse, opposite, adjacent) and learn the sine, cosine, and tangent ratios that link an acute angle to those side lengths.

Learn how to derive the exact trigonometric values at the special angles $30^\circ$, $45^\circ$, and $60^\circ$.

Learn the side ratios of the $45^\circ$-$45^\circ$-$90^\circ$ and $30^\circ$-$60^\circ$-$90^\circ$ triangles, and use them to find the exact trigonometric ratios at those angles for a triangle of any size.

Learn how to draw angles on the coordinate plane, identify their quadrants, and switch between equivalent measures of the same rotation in both degrees and radians.

Learn how to find the distance from the origin to any point using the Pythagorean theorem, why that gives the circle of radius $r$ the equation $x^2 + y^2 = r^2$, and how one comparison decides whether a point lies inside, on, or outside the circle.

Learn how angles on the coordinate plane correspond to points on the circle of radius $1$, why those coordinates are exactly the cosine and sine of the angle, and how to relate any angle back to its acute form.

Learn how to evaluate sine and cosine for any angle, including obtuse, negative, and angles exceeding one full revolution, by combining the reference angle with quadrant signs.

Learn how to build the sine and cosine graphs from the unit circle, identify their key points and shift relationship, and reason about the domain, range, and number of solutions to equations like $\sin\theta = c$.

Learn how to define tangent as $\sin\theta / \cos\theta$, read key features from its graph, and evaluate it at special angles.

Learn how to evaluate $\sec\theta$, $\operatorname{cosec}\theta$ and $\cot\theta$ as reciprocals of cosine, sine and tangent, and identify the angles at which each one is undefined.

Learn how to derive $\sin^2\theta + \cos^2\theta = 1$ from the unit circle, and use it to find one trigonometric ratio given the other and the quadrant.

Learn how to restrict $\sin$ to a domain where it is one-to-one, and use the resulting $\arcsin$ function to recover an angle from its sine.

Learn how to restrict $\cos$ to a domain where it is one-to-one, and use the resulting $\arccos$ function to recover an angle from its cosine.

Learn how to restrict $\tan$ to a domain where it is one-to-one, and use the resulting $\arctan$ function to recover an angle from its tangent.