Question

evaluate the sine, cosine, and tangent of the angle without using a calculator. (if an answer is undefined, enter undefined.) - 600° sin θ = cos θ = tan θ =

Explanation:

Explicación:

Paso 1: Reducir el ángulo a un ángulo entre 0° y 360°

Sabemos que - 600°+720° = 120°. Entonces, $\sin(-600^{\circ})=\sin(120^{\circ})$, $\cos(-600^{\circ})=\cos(120^{\circ})$ y $\tan(-600^{\circ})=\tan(120^{\circ})$.

Paso 2: Usar las identidades trigonométricas de ángulos especiales

Sabemos que $120^{\circ}=180^{\circ} - 60^{\circ}$. Entonces:
$\sin(120^{\circ})=\sin(180^{\circ}-60^{\circ})=\sin(60^{\circ})=\frac{\sqrt{3}}{2}$
$\cos(120^{\circ})=\cos(180^{\circ}-60^{\circ})=-\cos(60^{\circ})=-\frac{1}{2}$
$\tan(120^{\circ})=\frac{\sin(120^{\circ})}{\cos(120^{\circ})}=\frac{\frac{\sqrt{3}}{2}}{-\frac{1}{2}}=-\sqrt{3}$

Respuesta:

$\sin(-600^{\circ})=\frac{\sqrt{3}}{2}$, $\cos(-600^{\circ})=-\frac{1}{2}$, $\tan(-600^{\circ})=-\sqrt{3}$

Answer:

Explicación:

Paso 1: Reducir el ángulo a un ángulo entre 0° y 360°

Sabemos que - 600°+720° = 120°. Entonces, $\sin(-600^{\circ})=\sin(120^{\circ})$, $\cos(-600^{\circ})=\cos(120^{\circ})$ y $\tan(-600^{\circ})=\tan(120^{\circ})$.

Paso 2: Usar las identidades trigonométricas de ángulos especiales

Sabemos que $120^{\circ}=180^{\circ} - 60^{\circ}$. Entonces:
$\sin(120^{\circ})=\sin(180^{\circ}-60^{\circ})=\sin(60^{\circ})=\frac{\sqrt{3}}{2}$
$\cos(120^{\circ})=\cos(180^{\circ}-60^{\circ})=-\cos(60^{\circ})=-\frac{1}{2}$
$\tan(120^{\circ})=\frac{\sin(120^{\circ})}{\cos(120^{\circ})}=\frac{\frac{\sqrt{3}}{2}}{-\frac{1}{2}}=-\sqrt{3}$

Respuesta:

$\sin(-600^{\circ})=\frac{\sqrt{3}}{2}$, $\cos(-600^{\circ})=-\frac{1}{2}$, $\tan(-600^{\circ})=-\sqrt{3}$