Trigonometric Functions

If \( \sin \theta = \frac{3}{5} \) and \( \theta \) is an acute angle, what is \( \cos \theta \)?

In a right triangle, if the angle \( \theta = 30^\circ \), what is \( \tan \theta \)?

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

Evaluate \( \sin^2 45^\circ + \cos^2 45^\circ \).

If \( \tan \theta = 1 \), what is the value of \( \theta \) in degrees (0° to 90°)?

In a right-angled triangle, the hypotenuse is 10 cm and one leg is 6 cm. Find \( \sin \theta \), where \( \theta \) is the angle opposite to the leg of length 6 cm.

If \( \cos \theta = \frac{12}{13} \) and \( \theta \) is acute, find \( \tan \theta \).

If \( \sin A = \frac{3}{5} \) and \( \cos B = \frac{5}{13} \), find \( \sin (A + B) \). Assume both \( A \) and \( B \) are acute.

Prove that \( \tan^2 \theta + 1 = \sec^2 \theta \) using trigonometric identities.

If \( \sin \theta = \frac{7}{25} \) and \( \theta \) is in the first quadrant, find \( \cot \theta \).