Write the ratios for sin X
and cos X
.
Right triangle XYZ with right angle Z is shown. XY is labeled 12. XZ is labeled 5. YZ is labeled start root 119 end root.
To find the ratios of sine and cosine:
Sine (sin) of angle X is equal to the length of the side opposite angle X (YZ) divided by the length of the hypotenuse (XY):
sin(X) = YZ / XY
Given that YZ is √119 and XY is 12:
sin(X) = (√119) / 12
Cosine (cos) of angle X is equal to the length of the side adjacent to angle X (XZ) divided by the length of the hypotenuse (XY):
cos(X) = XZ / XY
Given that XZ is 5 and XY is 12:
cos(X) = 5 / 12
Therefore, the ratios for sin X and cos X are:
sin(X) = (√119) / 12
cos(X) = 5 / 12