Question

What is the value of arctan(cos⁻¹(−1/2))?

Multiple Choice:
a. π/6​
b. π/4​
c. π​/3
d. 2π​/3
e. 5π/6​

Answer 1

The value of arctan(cos⁻¹(-1/2)) is -π/3.

Step-by-step explanation:

The value of arctan(cos⁻¹(-1/2)) can be determined by evaluating the angles involved. Let's break it down step by step:

1. Start with cos⁻¹(-1/2). The arccosine function returns an angle whose cosine is -1/2. We know that the cosine of π/3 is 1/2, and since the cosine function is an even function, we can conclude that the cosine of -π/3 is also 1/2. So, cos⁻¹(-1/2) = -π/3.
2. Now, evaluate arctan(-π/3). The arctan function returns an angle whose tangent is -π/3. We know that the tangent of -π/3 is negative square root of 3. So, arctan(-π/3) = -π/3.

Therefore, the value of arctan(cos⁻¹(-1/2)) is -π/3. None of the given multiple choice options match this value, so none of the given options are correct.