I need to know how to draw a triangle respective of the given question in trigonometry.                        Give some examples.

Asked by seeni2005 | 12th Aug, 2016, 11:48: AM

Expert Answer:

In ΔAMP is a right angle triangle,
base AM = x, perpendicular = PM = y, Hypotenuse AP = r
begin mathsize 12px style sinθ equals Perpendicular over Hypotenuse equals straight y over straight r
cosθ equals Base over Hypotenuse equals straight x over straight r
tanθ equals Perpendicular over Base equals straight y over straight x
cosecθ equals Hypotenuse over Perpendicular equals straight r over straight y
secθ equals Hypotenuse over Base equals straight r over straight x
cotθ equals Base over Perpendicular equals straight x over straight y
Example colon space
If space sinA equals 3 over 5 comma space find space cosa space and space tanA.
Solution colon space
sinA equals Perpendicular over Hypotenuse equals 3 over 5
rightwards double arrow When space we space draw space the space triangle space we space shall space write space our space perpendicular space equals space 3 space units space and space hypotenuse equals space 4 space units
So comma space if space ABC space is space straight a space right minus angled space triangle comma
end style
 
 
begin mathsize 12px style By space Pythagoras space theorem comma space we space have
AC squared equals AB squared plus BC squared
rightwards double arrow 5 squared equals AB squared plus 3 squared
rightwards double arrow AB squared equals 5 squared minus 3 squared equals 16
rightwards double arrow AB equals 4
when space we space consider space the space trigonometric space ratios space of space angle straight A comma space we space have comma
Base equals AB equals 4 comma space Perpendicular equals BC equals 3 comma space Hypotenuse equals AC equals 5
rightwards double arrow cosA equals Base over Hypotenuse equals 4 over 5 space space and space tanA equals Perpendicular over Base equals 3 over 5
end style
begin mathsize 12px style Example colon
In space straight a space increment ABC comma space right space angled space at space straight A comma space if space AB equals 5 comma space AC equals 12 space and space BC equals 13 comma space find space sinB comma space cos space straight C space and space tan space straight B.
Solution colon
With space reference space to space angle straight B comma space we space have
We space have space base space equals AB space equals space 5 comma space perpendicular space equals space AC space equals 12 space and space Hypotenuse space equals space BC equals space 13
rightwards double arrow sinB equals AC over BC equals 12 over 13
and space tanB equals AC over AB equals 12 over 5

With space reference space to space angle straight C comma space we space have
We space have space base space equals AC space equals space 12 comma space perpendicular space equals space AB space equals 5 space and space Hypotenuse space equals space BC equals space 13
rightwards double arrow cosC equals AC over BC equals 12 over 13
end style

Answered by Rebecca Fernandes | 13th Aug, 2016, 02:44: PM