Use the image below to answer the following question. Find the value of sin x° and cos y°. What relationship do the ratios of sin x° and cos y° share?

enter image source here

1 Answer
Feb 7, 2018

See below.

Explanation:

Form the diagram:

By Pythagoras's theorem:

PO^2=12^2+5^2=169PO2=122+52=169

PO=sqrt(169)=13PO=169=13

cos(y)=5/13cos(y)=513

sin(x)=5/13sin(x)=513

The ratios are the same

This is true for all right triangles.

enter image source here

From diagram:

sin(alpha)=a/csin(α)=ac

cos(beta)=a/ccos(β)=ac

sin(beta)=b/csin(β)=bc

cos(alpha)=b/ccos(α)=bc

For all right triangles:

sin(theta)=cos(90^@-theta)sin(θ)=cos(90θ)