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.

sin²$\theta$ + cos²$\theta$ =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), L-R Up

[HA(pi/2, und)],

(2pi/3,-2), (pi,-1), (4pi/3,-2), = n shape

[HA (3pi/2, 0)],

(5pi/3,2) (2pi,1) R-L Up

Csc(Cosecant) graph

[HA(0,und)],

(pi/6,2), (pi/2,1), (5pi/6,2), U Shape

[HA(pi,und)],

(7pi/6,-2), (3pi/2,-1), (11pi/6,-2), n Shape

[HA(2pi,und)]

cot Cotangent) graph

[HA(0,und)],

(pi/4,1), (pi/2,0), (3pi/4,-1), L-R Up-Down

[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

Sin(2$\theta$)

2sin$\theta$cos$\theta$

cos(2$\theta$)

cos²$\theta$-sin²$\theta$

1-2sin²$\theta$

2cos²$\theta$-1