in any right triangle, we know that the two other angles that are not the 90 degree angle are complementary.?

Question

use trig definition to prove that sine of one angle= cosine of the other angle or that this is a false statement.

Answer 1

sinA = opposite side to A / hypotenuse
= adjacent side to B / hypotenuse
= cosB.

QED.

Answer 2

Call one angle a and the other angle b. By definition a+b=90.

Furthermore, sin(90-x)=cos(x) [fundamental identity]
a=90-b
sin(a) = sin(90-b)
sin(a) = cos(b) .

Answer 3

The three sides of a triangle can be labeled A, B and C opposite from angles a, b and c respectively.
If we let c be the 90 degree angle then
Sin(a)=A/C
Cos(a)=B/C
Sin(b)=B/C
Cos(b)=A/C

since both Sin(a) and Cos(b) are equal to A/C they are equal to each other.

since both Cos(a) and Sin(b) are equal to B/C they are equal to each other

Answer 4

yes they a complementary because they are both 45 degree angles making them together 90 degrees