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The following are all angle measures (in degrees, rounded to the nearest tenth) whose tangent is -16 .
Which is the principal value of 
arctan(-16) ?
Choose 1 answer:
(A) 
-626.4^(@)
(B) 
-446.4^(@)
(C) 
-266.4^(@)
(D) 
-86.4^(@)

The following are all angle measures (in degrees, rounded to the nearest tenth) whose tangent is 16-16 .\newlineWhich is the principal value of arctan(16) \arctan (-16) ?\newlineChoose 11 answer:\newline(A) 626.4 -626.4^{\circ} \newline(B) 446.4 -446.4^{\circ} \newline(C) 266.4 -266.4^{\circ} \newline(D) 86.4 -86.4^{\circ}

Full solution

Q. The following are all angle measures (in degrees, rounded to the nearest tenth) whose tangent is 16-16 .\newlineWhich is the principal value of arctan(16) \arctan (-16) ?\newlineChoose 11 answer:\newline(A) 626.4 -626.4^{\circ} \newline(B) 446.4 -446.4^{\circ} \newline(C) 266.4 -266.4^{\circ} \newline(D) 86.4 -86.4^{\circ}
  1. Principal Value Range: The principal value of an arctan function is the value of the inverse tangent that lies between 90-90 degrees and 9090 degrees.
  2. Calculate arctan(16)\arctan(-16): To find the principal value of arctan(16)\arctan(-16), we can use a calculator or a computer to compute the inverse tangent of 16-16.
  3. Use Calculator: Using a calculator, we find that arctan(16)\arctan(-16) is approximately 86.4-86.4 degrees.
  4. Verify Principal Value: The principal value of arctan(16)\arctan(-16) must be in the range of 90-90 degrees to 9090 degrees, and since 86.4-86.4 degrees falls within this range, it is the correct principal value.

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