Answer:
The values reported by Uma, Salina, and Tamara are all possible values for inverse cosine
Step-by-step explanation:
Solution:-
- The solution to the inverse "cosine" problem would have a general form:
θ = cos^-1 ( a )
Where, a: Any arbitrary constant, - 1 < a < 1
- The value of θ = 52° was reported by Salina suggests that the answer lies in the first quadrant of a cartesian plane where ( sin (θ) , cos (θ) , tan (θ) ) have positive values for "a".
Hence, 0 < a < 1 , θ = 52°
- The value of θ = 128° was reported by Tamara suggests that the answer lies in the second quadrant of a cartesian plane where ( sin (θ) ) have positive values for "a" and (cos (θ) , tan (θ) have negative values for "a". So for cos (128):
Hence, -1 < a < 0 , θ = 128°
- The value of θ = 308° was reported by Uma suggests that the answer lies in the fourth quadrant of a cartesian plane where ( cos (θ) ) have positive values for "a" and (sin (θ) , tan (θ) have negative values for "a". So for cos (308):
Hence, 0 < a < 1 , θ = 308°
- The angle θ reported by Uma and Salina are similar solution because of property law of complementary angles:
cos (θ) = cos ( 360 - θ )
Where, θ = 52°, cos (52°) = cos( 308°) .. Uma and Salina conform
However, cos ( 180 - θ ) = - cos (θ)
cos(128) = - cos ( 52 ) .... Uma and Tamara conform.
