Can the sine and cosine of the same acute angle be equal at the same time a) 0.6 and 0.8 b) 7/25 and 24/25 c) 1/3 and 2/3

As we know, the sine and cosine of the same angle must obey the following equation:

sin ^ 2 a + cos ^ 2 a = 1.

1)

Let us determine whether it is possible for these functions of an acute angle to be equal to 0.6 and 0.8 (recall that for such an angle they must be strictly positive):

0.6> 0;

0.8> 0;

0.6 ^ 2 + 0.8 ^ 2 = 1.

Answer: Yes.

2)

Determine whether it is possible for these acute angle functions to be 7/25 and 24/25:

7/25> 0;

24/25> 0;

(7/25) ^ 2 + (24/25) ^ 2 = (49 + 576): 625 = 1.

Answer: Yes.

3)

Let us determine whether it is possible for these functions of an acute angle to be equal to 1/3 and 2/3:

1/3> 0;

2/3> 0;

(1/3) ^ 2 + (2/3) ^ 2 = 5/9.

Answer: No.