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The ans is [tex] \frac{4}{3} [/tex]

The given point is P(-3,-4)

Since x = -3 and y = -4, we find the radius from the origin, r
Then,  r = [tex] \sqrt{( -3)^{2} +(-4 )^{2}} [/tex]= 5
Thus, sinФ = y/r = -4/5cosФ = x/r = -3/5
And, tanФ = [tex] \frac{sinФ}{cosФ} [/tex] = [tex] \frac{4}{3} [/tex] Ans. 

Answer:

The value of tanθ is 4/3.

Explanation:

It is given that the terminal side of an angle in standard position passes through P (-3,-4).

We need to find the value of tanθ.

Draw a perpendicular line on the x-axis from the point P(-3,-4).

Let θ is the terminal angle.

In a right angled triangle

[tex]\tan \theta=\dfrac{opposite}{adjacent}[/tex]

[tex]\tan \theta=\dfrac{4}{3}[/tex]

P(-3,-4) lies in 3rd quadrant. The value of tanθ is positive in first and 3rd quadrant.

Therefore, the value of tanθ is 4/3.

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