VerifiedNykia
  • VerifiedNykia
if tan θ = 12/5 and cos θ<0, what is sin θ?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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VerifiedNykia
  • VerifiedNykia
these are the choices https://gyazo.com/28d732e17e4f4c5ffd4ee0233aa34194
Michele_Laino
  • Michele_Laino
hint: using data of the exercise, we have the subsequent drawing: |dw:1449945698609:dw| namely the subsequent condition holds: \(\pi < \theta <3 \pi/2\)
Michele_Laino
  • Michele_Laino
now we have to apply this condition: \[{\left( {\cos \theta } \right)^2} + {\left( {\sin \theta } \right)^2} = 1\] where: \[\sin \theta = \frac{5}{{12}}\cos \theta \] please replace \(\sin \theta\) from second formula into the first one, and solve for \(\cos \theta\)

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Michele_Laino
  • Michele_Laino
oops.. the second formula, is: \[\sin \theta = \frac{{12}}{5}\cos \theta \]
Michele_Laino
  • Michele_Laino
and here is the right drawing: |dw:1449946149409:dw|
Michele_Laino
  • Michele_Laino
hint: another procedure, can be this: after the subsequent substitution: \[\cos \theta = \frac{5}{{12}}\sin \theta \] we get: \[{\left( {\frac{5}{{12}}\sin \theta } \right)^2} + {\left( {\sin \theta } \right)^2} = 1\] please solve for \(\sin \theta\)

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