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Problem of the Day #290: Sinusoidal Approximation January 3, 2012

Posted by Saketh in : potd , 2 comments

Using the fact that $\pi \approx \frac{22}{7}$, estimate the value of $\sin(11)$.

Problem of the Day #94: Fractional Trigonometry June 21, 2011

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Given that $x = \pi^{\pi^{\pi}}$, evaluate $$ \frac{1}{\frac{1}{4}(\sin^4{x}+\cos^4{x})-\frac{1}{6}(\sin^6{x}+\cos^6{x})} $$

Problem of the Day #87: Sinusoidal Thoughts June 14, 2011

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The expression $(\sin{x}+\cos{x})^n$ can be written as $k(n)\cdot\sin^n\left(f(x)\right)$, where $k(n)$ is a function of $n$ and $f(x)$ is a polynomial in $x$. Compute $k(10)$.

Problem of the Day #80: Tangential Thoughts June 7, 2011

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Let $f$ be the function defined as follows: $$f(0) = 1$$ $$f(n) = (1+\tan{n^\circ})f(n-1)$$ Given that $\log_2{f(45)}$ is an integer, compute its exact value.

Problem of the Day #74: Polynomials and Trigonometric Expressions June 1, 2011

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Evaluate $3x^4 + 2x^2y^2 – y^4 – y^2 + 4$ if $x = \sin \left(\frac{71\pi}{7919}\right)$ and $y = \cos \left(\frac{71\pi}{7919} \right)$.

Problem of the Day #65: Trigonometric Expressions and Factorials May 23, 2011

Posted by Alex in : potd , add a comment

Evaluate $2b^4 + 2a^2b^2 + a^2 – b^2 + 567$ if $a = \cos(567!)$ and $b = \sin(567!)$.