Step 2: Complete the trigonometric ratios
Now we can complete the trigonometric ratios for:
sin=opposite
hypotenuse=
CB
AC
cos=adjacent
hypotenuse=
AB
AC
tan=
opposite
adjacent=
CB
AB
Therefore to findsinwe would use sidesCB(opposite side to) andAC(hypotenuse). To findcoswe
would use sidesAB(adjacent side to) andAC(hypotenuse). To findtanwe would use sidesCB(opposite
side to) andAB(adjacent side to).
And then we can complete the trigonometric ratios for. For angle the opposite and adjacent sides switch
places (redraw the triangle above to help you see this). Notice how the hypotenuse is stillAC.
sin =opposite
hypotenuse=
AB
AC
cos =adjacent
hypotenuse=
CB
AC
tan =
opposite
adjacent=
AB
CB
Therefore to findsin we would use sidesAB(opposite side to ) andAC(hypotenuse). To findcos we
would use sidesCB(adjacent side to ) andAC(hypotenuse). To findtan we would use sidesAB(opposite
side to ) andCB(adjacent side to ).
Exercise 5 – 1:
1.Complete each of the following: AC B
a) sinA^= b)cosA^= c) tanA^=
d)sinC^= e)cosC^= f) tanC^=
2.In each of the following triangles, state whethera,bandcare the hypotenuse, opposite or adjacent sides
of the triangle with respect to.a)
戀愀 挀
b)挀
愀 戀
112 5.3. Defining the trigonometric ratios