anemone said:Given that \(\displaystyle \frac{\sin 3x}{\sin x}=\frac{6}{5}\), what is the ratio of \(\displaystyle \frac{\sin 5x}{\sin x}\)?
kaliprasad said:$\frac{\sin\, 3x}{\sin\, x}=\frac{6}{5}$ given
subtract 1 from both sides
$\frac{\sin\, 3x - \sin\, x}{\sin\, x}=\frac{1}{5}$
or $\frac{2 \sin\, x \cos\, 2x}{\sin\, x}=\frac{1}{5}$
or $\cos \, 2x = \frac{1}{10}\cdots(1)$
now
$\frac{\sin\, 5x + \sin \,x }{\sin x} = \frac{2 \sin\,3x \cos \,2x }{\sin x}$
$=2 \cos \,2x \frac{\sin\,3x}{\sin x}$
$=2 * \frac{1}{10} * \frac{6}{5} = \frac{6}{25}$
hence $\frac{\sin\, 5x}{\sin x} = \frac{6}{25} - 1 = - \frac{19}{25}$
The Trigonometric Challenge is a mathematical problem-solving game that involves using trigonometric functions such as sine, cosine, and tangent to solve various puzzles and challenges.
Anyone with a basic understanding of trigonometric functions can play the Trigonometric Challenge. It is suitable for students, teachers, and anyone interested in learning or practicing their trigonometry skills.
To play the Trigonometric Challenge, you need to solve a series of puzzles and challenges by using trigonometric functions. These challenges can be solved using a pencil and paper or a scientific calculator.
Playing the Trigonometric Challenge can help improve your problem-solving skills, strengthen your understanding of trigonometric functions, and enhance your mathematical reasoning abilities.
You can find the Trigonometric Challenge online on various websites, or you can purchase a physical copy of the game from educational stores or online retailers.