Quant · Geometry

Trigonometry

4 sub-topics · 42 lessons · 99 questions · 18 PYQs

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Trigonometric Identities16 lessons · 32 questions · 8 PYQs

Trigonometric Equations and Ranges9 lessons · 24 questions · 5 PYQs

Trigonometry in Triangles8 lessons · 20 questions · 2 PYQs

Heights and Distances9 lessons · 23 questions · 3 PYQs

Formula sheet

Complementary angles of elevation
$\theta+\phi=90^\circ:\ h=\sqrt{ab}$
Tangent of a sum or difference
$\tan(A\pm B)=\dfrac{\tan A\pm\tan B}{1\mp\tan A\tan B}$
Range of a weighted square sum
$a\sin^{2}\theta+b\cos^{2}\theta\in[\min(a,b),\max(a,b)]$
Sine rule
$\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}=2R$
Product of three cosines
$\cos x\cos(60^\circ-x)\cos(60^\circ+x)=\tfrac{1}{4}\cos 3x$
Range of a sine plus cosine
$-\sqrt{a^{2}+b^{2}}\le a\sin\theta+b\cos\theta\le\sqrt{a^{2}+b^{2}}$
Cosine rule
$a^{2}=b^{2}+c^{2}-2bc\cos A,\quad \cos A=\dfrac{b^{2}+c^{2}-a^{2}}{2bc}$
Range under a sum constraint
$\cos x+\cos y=c\Rightarrow(\sin x-\sin y)^{2}=2+2\cos(x+y)-c^{2}\le 4-c^{2}$