Question

Determine if true or false for each question:

For an angle A in standard position, if sinA = cosA then the terminal arm of the angle lies in quadrant II or IV

For an angle A in standard position, if sinA = -cosA then the terminal arm of the angle lies in quadrant I or III

Answer 1

the sine is positive in both I and II
the cosine is positive in both I and IV

the sine is negative in both III and IV
the cosines is negative in both II and III

so sin A = cos A in only I and III , so your first statement is false.


Repeat the same argument for the 2nd question.

Answer 2

Okay so if I apply that logic to the second statement, the sine will stay the same but the quadrants for the negatives and positives of cosine will swap.

the sine is positive in both I and II
the -cosine is positive in both II and III

the sine is negative in both III and IV
the -cosines is negative in both I and IV

That means sinA = -cosA is only in II and IV, making the second statement also false.

Answer 3

Right