Answer:
Part a) [tex]cos(A)=sin(B)[/tex]
Part b) [tex]cos(B)=sin(A)[/tex]
Part c) [tex]sin(A)=cos(B)[/tex]
Part d) [tex]sin(B)=cos(A)[/tex]
Step-by-step explanation:
we know that
In the right triangle ABC of the figure
[tex]A+B=90\°[/tex] ----> by complementary angles
so
[tex]cos(A)=sin(B)[/tex]
[tex]sin(A)=cos(B)[/tex]
Part a) Cos(A)
[tex]cos(A)=sin(B)[/tex]
[tex]cos(A)=\frac{5}{13}[/tex]
The value of cosine of angle A is the ratio between the adjacent side angle A to the hypotenuse
Part b) Cos(B)
[tex]cos(B)=sin(A)[/tex]
[tex]cos(B)=\frac{12}{13}[/tex]
The value of cosine of angle B is the ratio between the adjacent side angle B to the hypotenuse
Part c) Sin(A)
[tex]sin(A)=cos(B)[/tex]
[tex]sin(A)=\frac{12}{13}[/tex]
The value of sine of angle A is the ratio between the opposite side angle A to the hypotenuse
Part d) Sin(B)
[tex]sin(B)=cos(A)[/tex]
[tex]sin(B)=\frac{5}{13}[/tex]
The value of sine of angle B is the ratio between the opposite side angle B to the hypotenuse
