How to find exact value of arcsecx

Question

I need to find the exact value for these. 

 

1) arcsec ( -2) 

2) arcsec( -2/sqrt(3))

 

I know how to find exact values for arctan,arcsin and arccos but I dont know how to do it for arcsec.

Answer 1

Same concept.

arcsec(-2) = y 

means secy= -2

which means 

1/cosy =-2 which means

cosy = -1/2

 

what is arccos(-1/2)?

Answer 2

1)

Let arcsec(-2) = X

 

Applying sec on both sides  

 

sec( arc sec -2)  = sec X

 

so sec X = -2 Find the value of X (using cos X = -1/2)

2) 

Let arcsec(-2/sqrt3) = Y

 

Taking sec on both sides

secarc(-2/sqrt3) = sec Y

sec Y = -2/sqrt 3 or

cos Y = - sqrt (3)/2 Now finf Y