Inverse Circular Function

Ram Lama

Student

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Find the value of cos-1 (1/2) + 2 sin-1 (1/2)

  • 25 Dec, 2023
Replies (2)
Vidhyamath Online

Instructor

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Solution:

First, solve for cos-1 (1/2):

Let us take, y = cos-1 (1/2)

This can be written as:

cos y = (1/2)

cos y = cos (π /3).

Thus, the range of principal value of cos-1 is [0, π ]

Therefore, the principal value of cos-1 (1/2) is π/3.

Now, solve for sin-1 (1/2):

Let y = sin-1 (1/2)

sin y = 1/2

sin y = sin ( π/6)

Thus, the range of principal value of sin-1 is [(-π)/2, π/2 ]

Hence, the principal value of  sin-1 (1/2) is π/6.

Now we have cos-1 (1/2) = π/3 & sin-1 (1/2) = π/6

Now, substitute the obtained values in the given formula, we get:

= cos-1 (1/2) + 2sin-1 (1/2)

= π /3 + 2( π/6)

= π/3 + π/3

= ( π+π )/3

= 2π /3

Thus, the value of cos-1 (1/2) + 2 sin-1 (1/2) is  2π /3.

:) Happy Learning

  • 25 Dec, 2023
Vidhyamath Online

Instructor

  • 45
  • 0

Practice Problems

Solve the problems given below:

  1. Find the principal value of tan-1 (1).
  2.  If tan-1 (x − 1)/(x − 2) + tan-1 (x + 1)/(x + 2) = 𝜋/4, then find the value of x.
  3. Solve: tan-1 2x + tan-1 3x = π/4

  • 25 Dec, 2023

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