Three of these are wrong. Find the one that holds.

Exercise and reference answers

Questions

1. Question

   Three of these statements about sin⁻¹ are false.

   Choices

   1. Item

      Its principal range is [−π/2, π/2]

      Correct

      Yes

   2. Explanation

      That is the range of cos⁻¹, not sin⁻¹.

      Item

      Its principal range is [0, π]

   3. Explanation

      That is (sin x)⁻¹. The −1 here means inverse function.

      Item

      It equals 1/sin x

   4. Explanation

      Sine only outputs [−1, 1], so the inverse accepts only that.

      Item

      It is defined for every real x

2. Question

   Three of these statements about sec⁻¹ are false.

   Choices

   1. Item

      Its principal range is [0, π] − {π/2}

      Correct

      Yes

   2. Explanation

      sec is undefined at π/2, so that point must be removed.

      Item

      Its principal range is [0, π]

   3. Explanation

      That is where sec⁻¹ is NOT defined. Its domain is R − (−1, 1).

      Item

      Its domain is [−1, 1]

   4. Explanation

      cosec⁻¹ removes 0. sec⁻¹ removes π/2.

      Item

      It removes 0 from its range

Explanation