Question

writing trigonometric ratios
consider △xyz.
what are the ratios of sine, cosine, and tangent for angle y?
sin (y) = \frac{yz}{xy}; cos (y) = \frac{xz}{xy}; tan (y) = \frac{xz}{yz}
sin (y) = \frac{xz}{xy}; cos (y) = \frac{yz}{xy}; tan (y) = \frac{yz}{xz}

Explanation:

Step1: Recall trigonometric - ratio definitions

In a right - triangle $\triangle XYZ$ with right - angle at $Z$, for an acute angle $Y$, $\sin(Y)=\frac{\text{opposite}}{\text{hypotenuse}}$, $\cos(Y)=\frac{\text{adjacent}}{\text{hypotenuse}}$, and $\tan(Y)=\frac{\text{opposite}}{\text{adjacent}}$.
The side opposite to angle $Y$ is $XZ$, the side adjacent to angle $Y$ is $YZ$, and the hypotenuse is $XY$.

Step2: Calculate sine of angle $Y$

$\sin(Y)=\frac{XZ}{XY}$

Step3: Calculate cosine of angle $Y$

$\cos(Y)=\frac{YZ}{XY}$

Step4: Calculate tangent of angle $Y$

$\tan(Y)=\frac{XZ}{YZ}$

Answer:

$\sin(Y)=\frac{XZ}{XY};\cos(Y)=\frac{YZ}{XY};\tan(Y)=\frac{XZ}{YZ}$