Question

chapter 6 review score: 70/100 answered: 7/10 question 6 find an angle θ with 0° < θ < 360° that has the same sine as 250° θ = degrees cosine as 250° θ = degrees question help: post to forum

Explanation:

Step1: Recall sine - angle relationship

The sine function has the property $\sin\theta=\sin(180^{\circ}-\alpha)$ for an angle $\alpha$ in the second - quadrant. Given $\alpha = 250^{\circ}$, which is in the third - quadrant. We know that $\sin\theta=\sin(180^{\circ}+ \beta)$ where $\beta = 70^{\circ}$ ($250^{\circ}=180^{\circ}+70^{\circ}$), and also $\sin\theta=\sin(360^{\circ}-\beta)$ for angles in the fourth - quadrant. The angle with the same sine value as $250^{\circ}$ in the range $0^{\circ}<\theta<360^{\circ}$ is $\theta = 110^{\circ}$ since $\sin(250^{\circ})=\sin(180^{\circ} + 70^{\circ})=-\sin70^{\circ}$ and $\sin(110^{\circ})=\sin(180^{\circ}-70^{\circ})=\sin70^{\circ}$.

Step2: Recall cosine - angle relationship

The cosine function has the property $\cos\theta=\cos(360^{\circ}-\alpha)$ for an angle $\alpha$. Given $\alpha = 250^{\circ}$, the angle with the same cosine value as $250^{\circ}$ in the range $0^{\circ}<\theta<360^{\circ}$ is $\theta = 110^{\circ}$ because $\cos(250^{\circ})=\cos(360^{\circ}-110^{\circ})=\cos110^{\circ}$.

Answer:

Sine: $110$
Cosine: $110$