The value of [tex]cos\theta[/tex] will be [tex]-0.7813[/tex].
If the point [tex](-5.-4)[/tex] were rotated around the origin, it would form a circle of radius [tex]r[/tex]. Also, if the point were projected to the x-axis, a right-angled triangle would be formed. Then, the value of [tex]cos\theta[/tex], could be obtained by the formula
[tex]cos\theta=\dfrac{x}{r}[/tex]
where
[tex]x=\text{the side of the triangle opposite the reference angle of }\theta\\r=\text{the radius of the circle}[/tex]
From the point on the terminal side
[tex](x,y)=(-5,-4)[/tex]
we can directly get the value of [tex]x[/tex]. But we need to calculate the value of [tex]r[/tex].
To calculate the value of [tex]r[/tex], make use of Pythagoras theorem
[tex]r=\sqrt{x^2+y^2}\\=\sqrt{(-5)^2+(-4)^2}\\=\sqrt{25+16}\\\approx6.4[/tex]
We can now proceed to find the value of [tex]cos\theta[/tex], since we have the values of [tex]x[/tex], and [tex]r[/tex]. Therefore,
[tex]cos\theta=\dfrac{x}{r}\\\\=\dfrac{-5}{6.4}\approx-0.7813[/tex]
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