Here are five trigonometry questions for you:

1. If \(\sin \theta = \frac{3}{5}\), find \(\cos \theta\) and \(\tan \theta\).

2. Solve for \(x\) in the equation \(\sin(2x) = \cos(x)\) for \(0 \leq x < 2\pi\).

3. Prove the identity: \(\sec^2 \theta - \tan^2 \theta = 1\).

4. Find the exact value of \(\sin(75^\circ)\) using the sum or difference formula for sine.

5. A right triangle has an angle of \(30^\circ\) and a hypotenuse of 10 units. Find the length of the opposite and adjacent sides.

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Would you like more details or help with solving any of these?

Here are 5 related questions you could explore:
1. What is the value of \(\tan \theta\) if \(\cos \theta = \frac{4}{5}\)?
2. How do you derive the double angle formulas for sine and cosine?
3. What are the solutions to \(\tan(x) = \sqrt{3}\) between \(0\) and \(2\pi\)?
4. How do you find the values of all six trigonometric functions of an angle in standard position?
5. Can you derive the identity \(\cos(A+B) = \cos A \cos B - \sin A \sin B\)?

**Tip**: Knowing the unit circle well can greatly improve your speed in solving trigonometric problems!

Explore five challenging trigonometry problems that cover key concepts such as sine, cosine, tangent, trigonometric identities, and the Pythagorean theorem. Solve equations and prove identities, suitable for students in Grades 10-12.

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