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Solving a "Harvard" University Entrance Exam Interview Question

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Solving a "Harvard" University Entrance Exam Interview Question
Learn how to solve by using advanced [Algebra / Exponents / Geometry] techniques! Try solving it yourself first, then watch the step-by-step solution to check your answer.

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20 Comments

@thabangmashishi4391 3 weeks ago

It was easy ah I did not even think

@marcinzych9282 1 month ago (edited)

Finally x=k(pi/2), where k is integer

@ПавелШанин-с5к 2 weeks ago

Да, нас сильно ругали за такое сокращение sin на sin. Отлучали, чтобы у cos и sin не сократить s.

@Zülülülülül 2 weeks ago

2k +2/8
6_4
10
Totem
%2.7

@donsena2013 1 month ago

By inspection, I discerned that X = n (π/2), n any integer

@DSBca-u9p 1 month ago

x can be any multiple of pi/2 since if cos^2=0 then sin^2=1 and vice versa. So x = k (pi/2) (k any integer) covers all solutions.

@williamscott6291 1 month ago

Very nice and very tricky. This is why I say leave math to the mathematicians, they know all the tricks.

@ChemistAIEduConsult 1 month ago

Great tricks

@yuvalmagen100 1 month ago

beautiful handwriting

@haihe324 1 month ago (edited)

@12:10 Are -π/2 + 2kπ and 3π/2 + 2kπ basically the same? SInce if k = 1 for -π/2 + 2kπ, then -π/2 + 2kπ = -π/2 + 2π = -π/2 + 4π/2 = 3π/2. This is same as 3π/2 + 2kπ when k = 0. I think you meant to say π/2 + 2kπ instead of -π/2 + 2kπ since π/2 (i.e., π/2 + 2kπ when k = 0) is definitely a solution. Notice that 7^[(cos (π/2))^2] + 7^[(sin (π/2))^2] = 7^(0^2) + 7^(1^2) = 7^0 + 7^1 = 1 + 7 = 8. Therefore, the solution set should be {πt/2 + 2kπ, for t = 0, 1, 2, 3 and k ∈ ℤ}.

@mikeblaszczak 3 weeks ago

How can it be that -7x - 1 = 7 ?

@RamKripal-g7c 1 month ago (edited)

90⁰ or 0०

@KaderMbarga 1 month ago

x=pi+k*pi ou x=0+k*pi

@MadeleineHaba-ku3ck 1 month ago

Viette ça allait être rapide pour résoudre l'équation

@978646 1 month ago

7^1 + 7^0 = 7 + 1 = 8
1) cos²x = 1
x = ±n180° (n ∈ N)
sin²x = 0
x = 90° ± n180° (n ∈ N)
2) cos²x = 0
x = ± n180° (n ∈ N)
sin²x = 1
x = 90° ± n180° (n ∈ N)
____________________
x = ± n90° (n ∈ N)