First question:

csc = 1 / sin, so

1 / sin x = 123 / 100

sin x = 100 / 123 = 0.813, so

x = 54.39 degrees, and 125.61 degrees (assuming 0 < x < 360)

Second question:

cot = 1 / tan, so

1 / tan x = 598 / 1000, so

tan x = 1000 / 598 = 1.6722

I think you can take it from here.

for Q.1 answer is 54.4 degree.

For Q.2 it is 59.12

cosecθ = 1/sinθ, thus

sinθ = 1/1.23 and

θ = arcsin(1/1.23) which you can look up in your calculator and subtract from 180 (or pi) for the first two quadrants

cotθ = 1/tanθ

so tanθ = 1/0.598

θ = arctan(1/0.598) in first quadrant and 180 (or pi) + this for third quadrant

Not sure whether you want degrees or radians.

(im using x for theta)

So, cosecant is the same thing as 1/sine.. so you do 1/sinx=1.23

Multiply both sides by sinx

1=1.23sinx

now divide by 1.23

You get a decimal, then do sin^-1 on your calculator for the answer.

The answer is 54.390 degrees for cscx=1.23. (approx)

For cotx=.598, do the same thing

1/tanx = .598

1= .598tanx

1/.598 = tanx

tan^-1 (1/.598) = x

x= 59.120 degrees (approx)

cscx = 1.23

sinx = 1/1.23

sinx = 0.949 radians

cotx = 0.598

tanx = 1/0.598

x = 1.032 radians