Given is Triangle ABC right-angled at B, write all the six trigonometric ratios
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We have,
sinA=
Hypotenuse
Perpendicular
=
5
3
So, we draw a right triangle right angled at B such that
Perpendicular =BC=3 unit and, Hypotenuse =AC=5 units.
By Pythagoras theorem, we have
AC
2
=AB
2
+BC
2
⇒5
2
=AB
2
+3
2
⇒AB
2
=25−9=16
⇒AB=
16
=4
When we consider the trigonometric ratios of ∠ C , we have
Base =BC=3, Perpendicular =AB=4, and Hypotenuse =AC=4
∴sinC=
Hypotenuse
Perpendicular
=
5
4
cosC=
Hypotenuse
Base
=
5
3
tanC=
Base
Perpendicular
=
3
4
cosecC=
Perpendicular
Hypotenuse
=
4
5
secC=
Base
Hypotenuse
=
3
5
and,
cotC=
Perpendicular
Base
=
4
3
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