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Fundamental Trigonometric Identities
These are your basic building blocks for solving trigonometric equations and understanding how the pieces fit together. Using these identities can make sense of even the scariest looking trig.
\[ \sin ^{ 2 }{ 1^{\circ} } +\sin ^{ 2 }{ 2^{\circ} } +\sin ^{ 2 }{ 3^{\circ} } + \ldots \\ +\sin ^{ 2 }{ 88^{\circ} } +\sin ^{ 2 }{ 89^{\circ} } +\sin ^{ 2 }{ 90^{\circ} } = \ ? \]
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by
Edgar de Asis Jr.
\[ \large \frac { \sin ^{ 2 }{ \theta } }{ 5 } =\frac { \cos ^{ 2 }{ \theta } }{ 6 }\]
If \(\theta \) is a positive acute angle that satisfies the equation above, find \(\sin { \theta }\).
Note: Give your answer to 3 decimal places.
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by
shivamani patil
\[ \displaystyle \sum_{k=1}^{50} \Bigg [ \bigg(1 + \tan(k^\circ)+\sec(k^\circ)\bigg)\ \bigg(1+\cot(k^\circ)-\csc(k^\circ) \bigg)\Bigg]=\ ? \ \]
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by
K. J. W.
\[ \Large \left(\sqrt{2+\sqrt{2}}\right)^{x} + \left(\sqrt{2-\sqrt{2}}\right)^{x} = 2^{x}\]
Find the sum of all real \(x\) that satisfy the equation above.
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by
Utsav Banerjee
\[ \large\frac { 1 }{ \cos ^{ 2 }{ \theta } } +\frac { 1 }{ 1+\sin ^{ 2 }{ \theta } } +\frac { 2 }{ 1+\sin ^{ 4 }{ \theta } } +\frac { 4 }{ 1+\sin ^{ 8 }{ \theta } } \]
If \( \large \sin ^{ 16 }{ \theta } = \frac { 1 }{ 5 } \), what is the value of the expression above?
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by
Fuad Muhammad