Question

chapter 5 review score: 75/100 answered: 8/10 question 6 score on last try: 5 of 10 pts. see details for more. at least one scored part is incorrect. jump to first changable incorrect part. next question get a similar question you can retry this question below find an angle θ with 0° < θ < 360° that has the same: sine as 250°: θ = degrees cosine as 250°: θ = 110 degrees question help: post to forum submit question

Explanation:

Step1: Recall sine - angle relationship

The sine function has the property $\sin\theta=\sin(180^{\circ}-\alpha)$ and $\sin\theta = \sin(180^{\circ}+\alpha)$. Given $\alpha = 250^{\circ}$, we know that $\sin\theta=\sin(250^{\circ})$. Since $\sin\theta=\sin(180^{\circ}+\beta)$ where $\beta = 70^{\circ}$, and also $\sin\theta=\sin(360^{\circ}- 70^{\circ})$. The angles with the same sine value as $250^{\circ}$ in the range $0^{\circ}<\theta<360^{\circ}$ can be found using the unit - circle property of the sine function. The reference angle of $250^{\circ}$ is $250^{\circ}-180^{\circ}=70^{\circ}$. The angle with the same sine value as $250^{\circ}$ in the given range is $110^{\circ}$ because $\sin(250^{\circ})=\sin(110^{\circ})$ (using $\sin(180^{\circ}-\alpha)=\sin\alpha$, here $\alpha = 70^{\circ}$).

Step2: Recall cosine - angle relationship

The cosine function has the property $\cos\theta=\cos(360^{\circ}-\alpha)$. Given $\alpha = 250^{\circ}$, then $\cos\theta=\cos(250^{\circ})$. The reference angle of $250^{\circ}$ is $250^{\circ}-180^{\circ}=70^{\circ}$. And $\cos(250^{\circ})=\cos(110^{\circ})$ (using $\cos(180^{\circ}-\alpha)=-\cos\alpha$ and $\cos(360^{\circ}-\alpha)=\cos\alpha$, and the fact that the cosine of an angle in the third - quadrant and its corresponding angle in the second - quadrant with the same reference angle have the same absolute value and the correct sign relationship). The angle with the same cosine value as $250^{\circ}$ in the range $0^{\circ}<\theta<360^{\circ}$ is $110^{\circ}$ as $\cos(250^{\circ})=\cos(110^{\circ})$.

Answer:

Sine as $250^{\circ}:\theta = 110$ degrees
Cosine as $250^{\circ}:\theta = 110$ degrees