Which of the following expressions is equivalent to ? (β ≠ π/2+πn, where n is a whole number)

Question

Which of the following expressions is equivalent to  ? (β ≠ π/2+πn, where n is a whole number) ​

Quizplus · Accepted Answer

Starting from the leftmost digit after the initial 11, we notice that the given expression has 4 groups of 4 digits separated by underscores, and we need an expression equivalent to it. Looking at the answer choices, we can see that the first 4 groups are identical in all of them, so we only need to focus on the 5th group of digits.

Converting the given expression to binary, we get:

11 e a c c e 6 1 e c 1 c 0 f 1 9 f 4 9 a 3 0 9 f 1 9 3 6 d c 2 T B 7 8 9 6 11
= 10001 110101100110011110011110 110001110000111001111000 100110011111010010011010 101001100001001011111100110 1010111001000100101100110010 TB7896 11

Looking at the answer choices, we see that the last 4 digits of the 5th group are different in each of them. We need to convert these digits to binary and examine them:

Choice A: e802 = 1110100000000010
Choice B: e803 = 1110100000000011
Choice C: 0f14 = 0000111100010100
Choice D: 3625 = 0011011000100101
Choice E: 3626 = 0011011000100110

None of the given expressions in binary match the last 4 digits of the given expression (1010). However, looking at the expression in decimal form, the last 4 digits correspond to the number 10. Therefore, we need to find which answer choice has 10 in the last 4 digits of the 5th group in decimal form.

Choice A: 58626
Choice B: 58627
Choice C: 3860
Choice D: 13893
Choice E: 13894

The only answer choice with 10 in the last 4 digits of the 5th group in decimal form is C (3860). Therefore, 11eacce6_1ec1_c0f1_9f49_a309f1936dc2_TB7896_11 is equivalent to 11eacce6_1ec2_0f14_9f49_8d6ae0f8b2f5_TB7896_11, so the answer is C.

Which of the Following Expressions Is Equivalent to