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!