Inverse Trigonometry

Domain

100

arc(tan)

R

200

arc(cot)

R

300

arc(sec)

R-(-1,1)

400

arc(cos)

[-1,1]

500

arc(cosec)

R-(-1,1)

Range

100

tan^-1

(-pi/2,pi/2)

200

arc(sin)

[-pi/2,pi/2]

300

arc(sec)

[0,pi]-{pi/2}

400

arc(cot)

(0,pi)

500

cosec^-1

[-pi/2,pi/2]-{0}

Find the principal value

100

tan^-1(sqrt3)

pi/3

200

sin^-1(-sqrt3/2)

-pi/3

300

cosec^-1(-sqrt2)

-pi/4

400

cos^-1(-1/2)

2pi/3

500

sec^-1(-2/sqrt3)

5pi/6