The trigonometric ratio cos θ is 3/5.
What is trigonometry?
Trigonometry is mainly concerned with specific functions of angles and their application to calculations. Trigonometry deals with the study of the relationship between the sides of a triangle (right-angled triangle) and its angles.
For the given situation,
The point on the terminal side is (3, -4)
⇒ [tex](x,y)=(3,-4)[/tex]
The diagram below shows the right angled triangle in which x axis is the base and the y axis is the perpendicular side of the triangle.
Now the other side r, hypotenuse can be found using the Pythagoras theorem,
[tex]Hypotenuse^{2}=base^{2} +perpendicular^{2}[/tex]
⇒ [tex]Hypotenuse^{2}=(3)^{2} +(-4)^{2}[/tex]
⇒ [tex]Hypotenuse=\sqrt{9+16}[/tex]
⇒ [tex]Hypotenuse=\sqrt{25}[/tex]
⇒ [tex]Hypotenuse=5[/tex]
Now, r = 5
Thus by trigonometric ratio,
[tex]cos \theta=\frac{base}{hypotenuse}[/tex]
⇒ [tex]cos \theta=\frac{3}{5}[/tex]
Hence we can conclude that the trigonometric ratio cos θ is 3/5.
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