Trigonometry

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

In a right triangle, if the length of the hypotenuse is 10 cm and one angle is 30°, what is the length of the side opposite to the 30° angle?

Find \( \tan 45^\circ \).

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

In \( \triangle ABC \), right angled at C, if \( \tan A = \frac{3}{4} \), find \( \sin B \).

Evaluate \( \sin 60^\circ \times \cos 30^\circ + \cos 60^\circ \times \sin 30^\circ \).

If \( \sin \theta = \frac{5}{13} \) and \( \theta \) is in the second quadrant, find \( \cos \theta \).

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

In \( \triangle ABC \), if \( \sin A = \frac{7}{25} \) and \( \cos B = \frac{24}{25} \), find \( \sin (A + B) \).

If \( \sin \theta = 0.6 \) and \( \theta \) lies in the third quadrant, find \( \tan \theta \).