Answer:
[tex]cos\theta = -\frac{12}{37}[/tex]
Step-by-step explanation:
Given
[tex]tan\theta = \frac{35}{12}[/tex]
Quadrant: 3rd
Required
Determine [tex]cos\theta[/tex]
This question will be solved using the Pythagoras theorem
[tex]Hyp^2 = Adj^2 + Opp^2[/tex]
The tangent of an angle is calculated as thus;
[tex]tan\theta = \frac{Opp}{Adj}[/tex]
Comparing
[tex]tan\theta = \frac{35}{12}[/tex] to [tex]tan\theta = \frac{Opp}{Adj}[/tex]
We can conclude that
[tex]Opp = 35[/tex] [tex]Adj = 12[/tex]
Substitute these values in the Pythagoras formula
[tex]Hyp^2 = 35^2 + 12^2[/tex]
[tex]Hyp^2 = 1225 + 144[/tex]
[tex]Hyp^2 = 1369[/tex]
Square root of both sides
[tex]Hyp = \sqrt{1369}[/tex]
[tex]Hyp = 37[/tex]
SInce [tex]\theta[/tex] is in the 3rd quadrant, then
[tex]cos\theta = -\frac{Adj}{Hyp}[/tex]
Where [tex]Adj = 12[/tex] and [tex]Hyp = 37[/tex]
[tex]cos\theta = -\frac{12}{37}[/tex]
