Getting Triggy with It #1

Geometry Level 2

Find the approximate value of cos ⁡ ( sin ⁡ ( tan ⁡ ( sin ⁡ ( cos ⁡ ( 0 ∘ ) ) ) ) ) \cos(\sin(\tan(\sin(\cos(0^\circ))))) to the nearest integer without a calculator.


The answer is 1.

Deva Craig by Deva Craig , 22, USA

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1 solution

Hana Wehbi
Feb 21, 2017

The cosine function alternates between 1 and -1 so the maximum value is 1.

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This is wrong. cos ⁡ ( sin ⁡ ( tan ⁡ ( sin ⁡ ( cos ⁡ ( 0 ∘ ) ) ) ) ) = 1 \cos(\sin(\tan(\sin(\cos(0^\circ))))) = 1 is definitely not true, because ( sin ⁡ ( tan ⁡ ( sin ⁡ ( cos ⁡ ( 0 ∘ ) ) ) ) (\sin(\tan(\sin(\cos(0^\circ)))) is not an integer.

Pi Han Goh - 4 years, 3 months ago

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I believe Hana answered the problem, considering the following expression ⌈ cos ⁡ ( sin ⁡ ( tan ⁡ ( sin ⁡ ( cos ⁡ ( 0 ∘ ) ) ) ) ) ⌉ \left\lceil \cos\left(\sin\left(\tan\left(\sin\left(\cos\left(0^{\circ}\right)\right)\right)\right)\right) \right\rceil . However, the solution is not rigorous and entirely correct since after evaluating cos ⁡ ( 0 ∘ ) \cos\left(0^{\circ}\right) , the function now depends on the value of radians. In addition, it takes some thoughts to understand the value within the trig, not quickly guessing the value based on the function's nature.

Michael Huang - 4 years, 3 months ago

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