An angle is in standard postion, such that sin $\theta$θ = $\frac{-5}{7}$−57 . What are the possible values of $\theta$θ , to the nearest degree, if 0 degrees $\le\theta<360$≤θ<360 degrees?
6 years ago
To solve this, just take the inverse sine of -5/7
$\sin^{-1}\left(\frac{-5}{7}\right)=-45.6$sin−1(−57 )=−45.6
Then adjust so that your answer falls within the bounds set out for you and find your other answer in quadrants III and IV:
$\theta_1=-45.6+270=224.4$θ1=−45.6+270=224.4
$\theta_2=-45.6+360=314.4$θ2=−45.6+360=314.4
6 years ago
Answered By Emily H
To solve this, just take the inverse sine of -5/7
$\sin^{-1}\left(\frac{-5}{7}\right)=-45.6$sin−1(−57 )=−45.6
Then adjust so that your answer falls within the bounds set out for you and find your other answer in quadrants III and IV:
$\theta_1=-45.6+270=224.4$θ1=−45.6+270=224.4
$\theta_2=-45.6+360=314.4$θ2=−45.6+360=314.4