How do you find the exact values of #costheta# and #sintheta# when #tantheta=5/12#?

2 Answers
bp
Nov 7, 2016

sinθ=#5/13#

and cosθ=#12/13#

Explanation:

Draw a right triangle with base 12 and height 5 units with angle #theta# sitting on the base as shown below
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Apply Pythagoras theorem to get hypotenuse= 13 units

Work out sin#theta= 5/13#

and cos#theta= 12/13#

Narad T.
Nov 7, 2016

#costheta=12/13# and #sin theta=5/13#

Explanation:

If #tantheta=5/12= (opposite side)/(adjacent side)#
So the hypotenuse #=sqrt(5^2+12^2)=sqrt169=13#
#costheta=#(adjacent side)/(hypotenuse)#=12/13#
#sintheta=#(opposite side)/(hypotenuse)#=5/13#

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