Evaluate the expression.Round your result to two decimal places. $\tan ^ { - 1 } ( - \sqrt { 588 } )$
A)-0.53
B)-1.53
C)0.47
D)-3.53
E)-2.53

Question

Evaluate the expression.Round your result to two decimal places.  $\tan ^ { - 1 } ( - \sqrt { 588 } )$  
A)-0.53
B)-1.53
C)0.47
D)-3.53
E)-2.53

Quizplus · Accepted Answer

The expression $\tan^{-1}(-\sqrt{588})$ can be simplified by recognizing that $\sqrt{588}$ simplifies to $\sqrt{4*147} = 2\sqrt{147}$. The arctan of a negative value will fall in either the second or fourth quadrant of the unit circle, where tangent values are negative. However, since arctan specifically returns values in the first and fourth quadrants for positive and negative inputs, respectively, we know the answer will be in the fourth quadrant, implying a negative angle close to 0 but not exceeding $-\frac{\pi}{2}$ or approximately -1.57. Among the options, -1.53 is the closest to this conceptual range, making it the correct choice.

Evaluate the Expression tan⁡−1(−588)\tan ^ { - 1 } ( - \sqrt { 588 } )tan−1(−588​)

Evaluate the Expression $\tan ^ { - 1 } ( - \sqrt { 588 } )$