(10.) which one of the following is positive? a. cos(5π/4) b. cot(-π/3) c. sin(-3π/4) d. sec(3π/2) -√2/2 =…

Explanation:

Step1: Analizar $\cos(\frac{5\pi}{4})$

$\cos(\frac{5\pi}{4})=\cos(\pi + \frac{\pi}{4})=-\cos(\frac{\pi}{4})=-\frac{\sqrt{2}}{2}<0$

Step2: Analizar $\cot(-\frac{\pi}{3})$

$\cot(-\frac{\pi}{3})=-\cot(\frac{\pi}{3})=-\frac{\cos(\frac{\pi}{3})}{\sin(\frac{\pi}{3})}=-\frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}}=-\frac{1}{\sqrt{3}}<0$

Step3: Analizar $\sin(-\frac{3\pi}{4})$

$\sin(-\frac{3\pi}{4})=-\sin(\frac{3\pi}{4})=-\frac{\sqrt{2}}{2}<0$

Step4: Analizar $\sec(\frac{3\pi}{2})$

$\sec(\frac{3\pi}{2})=\frac{1}{\cos(\frac{3\pi}{2})}$, y $\cos(\frac{3\pi}{2}) = 0$, entonces $\sec(\frac{3\pi}{2})$ está indefinido y no es positivo o negativo. Pero revisando los valores de las otras opciones, todas son negativas.

Answer: Ninguna de las opciones dadas es positiva.