GCSE Maths Formulas

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GCSE • Trigonometry
area triangle
\( A = \tfrac{1}{2}ab\sin C \)
GCSE • Trigonometry
non-right triangle
\( a^2=b^2+c^2-2bc\cos A \)
GCSE • Trigonometry
radians degrees
\( \text{radians}=\text{degrees}\times\tfrac{\pi}{180},\qquad \text{degrees}=\text{radians}\times\tfrac{180}{\pi} \)
GCSE • Trigonometry
sine cosine
\( \sin\theta=\tfrac{\text{opp}}{\text{hyp}},\quad \cos\theta=\tfrac{\text{adj}}{\text{hyp}},\quad \tan\theta=\tfrac{\text{opp}}{\text{adj}} \)
GCSE • Trigonometry
non-right triangle
\( \frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C} \)
GCSE • Trigonometry
exact values triangles
\( \sin45^{\circ}=\cos45^{\circ}=\tfrac{\sqrt{2}}{2};\;\sin30^{\circ}=\tfrac{1}{2},\;\cos30^{\circ}=\tfrac{\sqrt{3}}{2};\;\sin60^{\circ}=\tfrac{\sqrt{3}}{2},\;\cos60^{\circ}=\tfrac{1}{2} \)
GCSE • Trigonometry
identity ratio
\( \sin^2\theta+\cos^2\theta=1,\quad \tan\theta=\tfrac{\sin\theta}{\cos\theta} \)