Trigonometric Functions

If \( \sin \theta = \frac{3}{5} \) and \( \theta \) is in the first quadrant, what is \( \cos \theta \)?

Evaluate \( \tan 45^\circ + \cot 45^\circ \).

If \( \sin A = \frac{5}{13} \) and \( A \) is acute, find \( \tan A \).

If \( \sin \theta = \frac{1}{3} \) and \( \theta \) lies in the second quadrant, find \( \cos \theta \).

Find the value of \( \sin 75^\circ \) using angle addition formula.

If \( \tan \theta = 2 \), find \( \sin \theta + \cos \theta \).

Prove that \( 1 + \tan^2 A = \sec^2 A \).

If \( \sin A = \frac{12}{13} \) and \( A \) is in the second quadrant, find \( \cos A \) and \( \tan A \).

Solve for \( \theta \) in \( 0^\circ \leq \theta \leq 360^\circ \): \( 2 \sin^2 \theta - 3 \sin \theta + 1 = 0 \).