Question

Find the principal value of

(i) sin ^-1 (-1/ √2)

(ii) cos ^-1 (-√3/ 2)

(iii) tan ^-1 (-√3)

(iv) sec ^-1 (-2)

(v) cosec ^-1 (- √2)

(vi) cot ^-1 (-1/ √3)

Answer 1

(i) sin ^-1 (-1/ √2)

We know that

sin ^-1 (-1/ √2) = – sin ^-1 (sin π/4)

= – π/4

(ii) cos ^-1 (-√3/ 2)

We know that

cos ^-1 (-√3/ 2) = π – cos ^-1 (cos π/6)

= π – π/6

= 5π/6

(iii) tan ^-1 (-√3)

We know that

tan ^-1 (-√3) = – tan ^-1 (tan π/3)

= – π/3

(iv) sec ^-1 (-2)

We know that

sec ^-1 (-2) = π – sec ^-1 (sec π/3)

= π – π/3

= 2 π/3

(v) cosec ^-1 (- √2)

We know that

cosec ^-1 (- √2) = – cosec ^-1 (cosec π/4)

= – π/4

(vi) cot ^-1 (-1/ √3)

We know that

cot ^-1 (-1/ √3) = π – cot ^-1 (cot π/3)

= π – π/3

= 2 π/3