Question

Find the principal value of:

(i) sin ^-1 (√3/ 2)

(ii) sin ^-1 (1/2)

(iii) cos ^-1 (1/2)

(iv) tan ^-1 (1)

Answer 1

(i) sin ^-1 (√3/ 2)

We know that

sin ^-1 (√3/ 2) = sin ^-1 (sin π/3)

= π/3

(ii) sin ^-1 (1/2)

We know that

sin ^-1 (1/2) = sin ^-1 (sin π/6)

= π/6

(iii) cos ^-1 (1/2)

We know that

cos ^-1 (1/2) = cos ^-1 (cos π/3)

= π/3

(iv) tan ^-1 (1)

We know that

tan ^-1 (1) = tan ^-1 (tan π/4)

= π/4