📐 Trigonometry

Mathematics | FirstInTest

#	Trigonometry Formula	Notes	alternate formula
1(i)	$\sin x = \frac{1}{\csc x}$	—	$\csc x = \frac{1}{\sin x}$
1(ii)	$\cos x = \frac{1}{\sec x}$	—	$\sec x = \frac{1}{\cos x}$
1(iii)	$\cot x = \frac{1}{\tan x}$	—	$\tan x = \frac{1}{\cot x}$
1(iv)	$\tan x = \frac{\sin x}{\cos x}$	—	$\cot x = \frac{\cos x}{\sin x}$
1(v)	$\sin^2 x + \cos^2 x = 1$	—	—
1(vi)	$1 + \tan^2 x = \sec^2 x$	—	$\sec x - \tan x = \frac{1}{\sec x + \tan x}$
1(vii)	$1 + \cot^2 x = \csc^2 x$	—	$\csc x - \cot x = \frac{1}{\csc x + \cot x}$
2(i)	$\sin (-x) = -\sin x$	—	$\csc (-x) = -\csc x$
2(ii)	$\cos (-x) = \cos x$	—	$\sec (-x) = \sec x$
2(iii)	$\tan (-x) = -\tan x$	—	$\cot (-x) = -\cot x$
2(iv)	$\sin \left(\frac{\pi}{2} - x\right) = \cos x$	Co-function identity	—
2(iv)	$\cos \left(\frac{\pi}{2} - x\right) = \sin x$	Co-function identity	—
2(iv)	$\tan \left(\frac{\pi}{2} - x\right) = \cot x$	Co-function identity	—
2(iv)	$\sec \left(\frac{\pi}{2} - x\right) = \csc x$	Co-function identity	—
2(iv)	$\csc \left(\frac{\pi}{2} - x\right) = \sec x$	Co-function identity	—
2(iv)	$\cot \left(\frac{\pi}{2} - x\right) = \tan x$	Co-function identity	—
2(v)	$\sin \left(\frac{\pi}{2} + x\right) = \cos x$	Quadrant II transformation	—
2(v)	$\cos \left(\frac{\pi}{2} + x\right) = -\sin x$	Quadrant II transformation	—
2(v)	$\tan \left(\frac{\pi}{2} + x\right) = -\cot x$	Quadrant II transformation	—
2(v)	$\cot \left(\frac{\pi}{2} + x\right) = -\tan x$	Quadrant II transformation	—
2(v)	$\sec \left(\frac{\pi}{2} + x\right) = -\csc x$	Quadrant II transformation	—
2(v)	$\csc \left(\frac{\pi}{2} + x\right) = \sec x$	Quadrant II transformation	—
2(vi)	$\sin (\pi - x) = \sin x$	Quadrant II transformation	—
2(vi)	$\cos (\pi - x) = -\cos x$	Quadrant II transformation	—
2(vi)	$\tan (\pi - x) = -\tan x$	Quadrant II transformation	—
2(vi)	$\cot (\pi - x) = -\cot x$	Quadrant II transformation	—
2(vi)	$\sec (\pi - x) = -\sec x$	Quadrant II transformation	—
2(vi)	$\csc (\pi - x) = \csc x$	Quadrant II transformation	—
2(vii)	$\sin \left(\frac{3\pi}{2} - x\right) = -\cos x$	Quadrant III transformation	—
2(vii)	$\cos \left(\frac{3\pi}{2} - x\right) = -\sin x$	Quadrant III transformation	—
2(vii)	$\tan \left(\frac{3\pi}{2} - x\right) = \cot x$	Quadrant III transformation	—
2(vii)	$\cot \left(\frac{3\pi}{2} - x\right) = \tan x$	Quadrant III transformation	—
2(vii)	$\csc \left(\frac{3\pi}{2} - x\right) = -\sec x$	Quadrant III transformation	—
2(vii)	$\sec \left(\frac{3\pi}{2} - x\right) = -\csc x$	Quadrant III transformation	—
2(viii)	$\sin \left(\frac{3\pi}{2} + x\right) = -\cos x$	Quadrant IV transformation	—
2(viii)	$\cos \left(\frac{3\pi}{2} + x\right) = \sin x$	Quadrant IV transformation	—
2(viii)	$\tan \left(\frac{3\pi}{2} + x\right) = -\cot x$	Quadrant IV transformation	—
2(viii)	$\cot \left(\frac{3\pi}{2} + x\right) = -\tan x$	Quadrant IV transformation	—
2(viii)	$\csc \left(\frac{3\pi}{2} + x\right) = -\sec x$	Quadrant IV transformation	—
2(viii)	$\sec \left(\frac{3\pi}{2} + x\right) = \csc x$	Quadrant IV transformation	—
2(ix)	$\sin (2\pi - x) = -\sin x$	Quadrant IV transformation (periodic function)	—
2(ix)	$\cos (2\pi - x) = \cos x$	Quadrant IV transformation (periodic function)	—
2(ix)	$\tan (2\pi - x) = -\tan x$	Quadrant IV transformation (periodic function)	—
2(ix)	$\csc (2\pi - x) = -\csc x$	Quadrant IV transformation (periodic function)	—
2(ix)	$\sec (2\pi - x) = \sec x$	Quadrant IV transformation (periodic function)	—
2(ix)	$\cot (2\pi - x) = -\cot x$	Quadrant IV transformation (periodic function)	—
2(x)	Sine, Cosine, Cosecant, Secant functions are periodic with period $2\pi$.	—	Tangent and Cotangent functions are periodic with period $\pi$.
2(xi)	Cosine and Secant functions are even functions.	—	Sine, Cosecant, Tangent, Cotangent functions are odd functions.

← Back to All Sheets