Trigonometry summary

Key learning points

• $\sin^2\theta+\cos^2\theta=1$ and related $\tan$ identities.
• Solve by rearranging to one trig function, then list all solutions in the interval.
• Exact values for key angles are examinable.
• Use CAST or a sketch to find companion solutions.

Worked example 1 — Find a side

Opposite $x$, hypotenuse $10$, angle $30^\circ$. Find $x$.

Working

SOH.

Worked example 2 — Find an angle

Adjacent $4$, hypotenuse $8$. Find $\theta$.

Working

CAH.

Worked example 3 — Tangent

Opposite $3$, adjacent $3$. Find $\theta$.

Working

TOA.

Worked example 4 — Equation

Solve $\sin\theta=\frac{1}{2}$ for $0^\circ\le\theta\le 360^\circ$.

Working

Sine is positive in the first and second quadrants.

Scaffolded Learning Sheet and answers (PDFs)

This page is a short, searchable overview for revision and search engines. Use the Scaffolded Learning Sheet first, then the Answers PDF for a full written solution. The printable PDFs remain the main classroom resource.