Consider the following:

• tan(π/6)
• tan(3π/4)
• tan(5π/4)
• tan(2π/3)

What is the correct order?

• A: 1 < 4 < 2 < 3
• B: 4 < 2 < 1 < 3
• C: 4 < 2 < 3 < 1
• D: 1 < 4 < 3 < 2

To find the correct order of the given tangent values, let's first calculate each one:

Tangent Values

• tan(π/6): This equals 1/√3 or approximately 0.577.
• tan(3π/4): This is -1.
• tan(5π/4): This is also 1, but negative, so it equals -1.
• tan(2π/3): This equals -√3 or approximately -1.732.

Ordering the Values

Now, let's list the values in order from smallest to largest:

• tan(2π/3) ≈ -1.732
• tan(3π/4) = -1
• tan(5π/4) = -1
• tan(π/6) ≈ 0.577

Thus, the correct order of the tangent values is:

1. tan(2π/3)
2. tan(3π/4)
3. tan(5π/4)
4. tan(π/6)

In terms of the options provided, the correct answer is D: 1.