Pythagorean Identities
Simplify: \[ \sqrt{1 - \sin^2 \theta}. \]
by
Martin Soliman
\[ \large \frac { \sin ^{ 2 }{ \theta } }{ 5 } =\frac { \cos ^{ 2 }{ \theta } }{ 6 }\]
If \(\theta \) is a positive acute angle that satisfies the equation above, find \(\sin { \theta }\).
Note: Give your answer to 3 decimal places.
by
shivamani patil
Letting \[P=\sin A \sin B \\ Q= \sin C \cos A \\ R = \sin A \cos B \\ S=\cos A \cos C\]
Find the value of \(5(P^2+Q^2+R^2+S^2)\) .
by
Vaibhav Prasad
\[ \large\frac { 1 }{ \cos ^{ 2 }{ \theta } } +\frac { 1 }{ 1+\sin ^{ 2 }{ \theta } } +\frac { 2 }{ 1+\sin ^{ 4 }{ \theta } } +\frac { 4 }{ 1+\sin ^{ 8 }{ \theta } } \]
If \( \large \sin ^{ 16 }{ \theta } = \frac { 1 }{ 5 } \), what is the value of the expression above?
by
Fuad Muhammad
A triangle has sides of magnitude \(1\), \( \sin x\), and \(\cos x\).
where \(0 < x < \frac { \pi }{ 2 } .\)
Find the largest angle of the triangle in degrees.
Assume that the triangle is non-degenerate.
by
milind prabhu