ENTREGA INDIVIDUAL Parte 1: Grados y Radianes $$ \begin{array}{lll} ext { - Convierta de grados a radianes y viceversa } \ \begin{array}{lll} ext { 1. } 45^{\circ} & 2.90^{\circ} & ext { 3. } 60^{\circ} \ ext { 4. } \frac{\pi}{30} \mathrm{rad} & 5.7 \pi \mathrm{rad} & ext { 6. } 9 \mathrm{rad}\end{array}\end{array} $$.

Question

ENTREGA INDIVIDUAL Parte 1: Grados y Radianes $$ \begin{array}{lll}	ext { - Convierta de grados a radianes y viceversa } \ \begin{array}{lll}	ext { 1. } 45^{\circ} & 2.90^{\circ} & 	ext { 3. } 60^{\circ} \ 	ext { 4. } \frac{\pi}{30} \mathrm{rad} & 5.7 \pi \mathrm{rad} & 	ext { 6. } 9 \mathrm{rad}\end{array}\end{array} $$.

UpStudy AI · Accepted Answer

Para convertir entre grados y radianes, utilizamos las siguientes relaciones:

1. $$ 180^\circ = \pi \, \text{rad} $$
2. Para convertir de grados a radianes, usamos la fórmula:
   $$
   \text{radianes} = \text{grados} \times \frac{\pi}{180}
   $$
3. Para convertir de radianes a grados, usamos la fórmula:
   $$
   \text{grados} = \text{radianes} \times \frac{180}{\pi}
   $$

Ahora, procedamos con las conversiones solicitadas:

### De Grados a Radianes

1. **$$ 45^\circ $$**:
   $$
   45^\circ \times \frac{\pi}{180} = \frac{\pi}{4} \, \text{rad}
   $$

2. **$$ 90^\circ $$**:
   $$
   90^\circ \times \frac{\pi}{180} = \frac{\pi}{2} \, \text{rad}
   $$

3. **$$ 60^\circ $$**:
   $$
   60^\circ \times \frac{\pi}{180} = \frac{\pi}{3} \, \text{rad}
   $$

### De Radianes a Grados

4. **$$ \frac{\pi}{30} \, \text{rad} $$**:
   $$
   \frac{\pi}{30} \times \frac{180}{\pi} = 6^\circ
   $$

5. **$$ 7\pi \, \text{rad} $$**:
   $$
   7\pi \times \frac{180}{\pi} = 1260^\circ
   $$

6. **$$ 9 \, \text{rad} $$**:
   $$
   9 \times \frac{180}{\pi} \approx 515.66^\circ
   $$

### Resumen de Resultados

- $$ 45^\circ = \frac{\pi}{4} \, \text{rad} $$
- $$ 90^\circ = \frac{\pi}{2} \, \text{rad} $$
- $$ 60^\circ = \frac{\pi}{3} \, \text{rad} $$
- $$ \frac{\pi}{30} \, \text{rad} = 6^\circ $$
- $$ 7\pi \, \text{rad} = 1260^\circ $$
- $$ 9 \, \text{rad} \approx 515.66^\circ $$
- De grados a radianes: 45° = π/4 rad, 90° = π/2 rad, 60° = π/3 rad. De radianes a grados: π/30 rad = 6°, 7π rad = 1260°, 9 rad ≈ 515.66°.

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