don't worry be happy smile love To find the trigonometric values of cosecant secant and cotangent for 30 degrees 60 degrees we can first sine cosine tangent these angles using unit circle or identities then take reciprocals to get cotangent. 1. For degrees: - \( \sin(30^\circ) = \frac{1}{2} \) \cos(30^\circ) \frac{\sqrt{3}}{2} \tan(30^\circ) \frac{1}{\sqrt{3}} \frac{\sqrt{3}}{3} Now cotangent: \csc(30^\circ) \frac{1}{\sin(30^\circ)} \frac{1}{1/2} 2 \sec(30^\circ) \frac{1}{\cos(30^\circ)} \frac{1}{\sqrt{3}/2} \frac{2}{\sqrt{3}} \frac{2\sqrt{3}}{3} \cot(30^\circ) \frac{1}{\tan(30^\circ)} \frac{1}{\sqrt{3}/3} \frac{3}{\sqrt{3}} \sqrt{3} 2. \sin(60^\circ) \cos(60^\circ) \tan(60^\circ) \csc(60^\circ) \frac{1}{\sin(60^\circ)} \sec(60^\circ) \frac{1}{\cos(60^\circ)} \cot(60^\circ) \frac{1}{\tan(60^\circ)} Therefore are: \(\csc(30^\circ) 2\) \(\sec(30^\circ) \frac{2\sqrt{3}}{3}\) \(\cot(30^\circ) \sqrt{3}\). \(\csc(60^\circ) \(\sec(60^\circ) \(\cot(60^\circ) \frac{\sqrt{3}}{3}\).