Question

URGENT
If 90°≤A≤180° and sin(A) = 4/7, then determine the exact values of cos(A) and tan(A).

Answer 1

If A is between the angles 90° and 180°, and we know that:

Sin(A) = 4/7.

But here we have an obvious problem, in the second quadrant, Sin(X) can only have negative values, and we know that 4/7 is a positive number

This means that the actual value of A is not a real value.

If we use the relation:

Asin(Sin(A)) = A = Asin(4/7) = 37°

We would find that A must be smaller than 90°.

And for the periodicity of the trigonometric functions, the next possible value for A will be 37° + 360° = 397°, that is bigger than 180°

And as the Value of A does not exist, the same happens for Cos(A) and tan(A)