1) If the Sin(70 degrees)= Cos(A), what must A be?
2) Why is the Sine of 10 degrees the same as the Cosine of 80 degrees?
20
the co- in cosine means sine of the complementary angle.
If cos(90-A) = cos90cosA + sin90sinA = sinA
cos 20
they are the same because they are complementary angles.
70 + 20 = 90
80 + 10 = 90
To find the value of A in the equation Sin(70 degrees) = Cos(A), we can use the fact that Sin(x) = Cos(90 degrees - x).
1) Sin(70 degrees) = Cos(90 degrees - 70 degrees)
= Cos(20 degrees)
Therefore, A must be equal to 20 degrees.
To understand why the sine of 10 degrees is the same as the cosine of 80 degrees, we need to know that the sine function is symmetrical around the point (45 degrees, 0.7071) on the unit circle, and the cosine function is symmetrical around the point (45 degrees, 0.7071) in the opposite direction.
2) Since the sine function is symmetrical around the point (45 degrees, 0.7071), we can say that Sin(10 degrees) = Cos(90 degrees - 10 degrees)
= Cos(80 degrees)
Hence, the sine of 10 degrees is the same as the cosine of 80 degrees.