Question

Which value is similar to sin^-1sin(6 π/7)?

(a) sin^-1(π/7)

(b) cos^-1(π/7)

(c) sin^-1(2π/7)

(d) coses^-1(π/7)

The question was posed to me in unit test.

This intriguing question comes from Inverse Trigonometry topic in section Inverse Trigonometric Functions of Mathematics – Class 12

Answer 1

Correct choice is (a) sin^-1(π/7)

The best explanation: sin^-1sin(6 π/7)

Now, sin(6 π/7) = sin(π – 6 π/7)

  = sin(2π + 6 π/7) = sin(π/7)

  = sin(3π – 6 π/7) = sin(20π/7)

  = sin(-π – 6 π/7) = sin(-15π/7)

  = sin(-2π + 6 π/7) = sin(-8π/7)

  = sin(-3π – 6 π/7) = sin(-27π/7)

Therefore, sin^-1sin(6 π/7) = sin^-1(π/7).