Equivalent Representations of Trig Functions

sec theta and secx

1/cos theta and 1/cos x

cos \theta and cos x

1/sec \theta and 1/sec x

csc theta and cscx

1/sin theta and 1/sin x

sin theta and sinx

1/ csc theta and 1/csc x

cot theta

1/ tan theta = cos theta/ sin theta

tan \theta

1/ cot theta = sin theta/ cos theta

tan x

1/ cot x = sin x/ cos x

cotx

1/ tan x = cos x/ sin x

sin² \theta + cos² \theta = 1

sin² \theta = 1 - cos² \theta is the Pythagorean identity in trigonometry, representing the relationship between the sine and cosine of an angle.

sin²theta + cos²theta =1 when you divide by sin

you obtain the identity 1 + \cot^2\theta = \csc^2\theta.

sin² \theta + cos² \theta =1 when you divide both sides by cos² \theta

you obtain the identity tan^2\theta+1=\sec\theta .

Sec (Secant) graph

(0,1) (pi/3,2), [HA(pi/2, und)], (2pi/3,-2), (pi,-1), (4pi/3,-2), [HA (3pi/2, 0)], (5pi/3,2) (2pi,1)

Csc(Cosecant) graph

[HA(0,und)], (pi/6,2), (pi/2,1), (5pi/6,2), [HA(pi,und)], (7pi/6,-2), (3pi/2,-1), (11pi/6,-2), [HA(2pi,und)]

cot Cotangent) graph

[HA(0,und)], (pi/4,1), (pi/2,0), (3pi/4,-1), [HA(pi,und)],

Inverse cosx / arccosx

inverse sin sqrt 1-x² and arcsin sqrt 1-x²

inverse sin and arcsinx

inverse cos sqt 1-x² and arccos sqrt 1-x²