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)
⇒ \((x,y)=(3,-4)\)
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,
\(Hypotenuse^{2}=base^{2} +perpendicular^{2}\)
⇒ \(Hypotenuse^{2}=(3)^{2} +(-4)^{2}\)
⇒ \(Hypotenuse=\sqrt{9+16}\)
⇒ \(Hypotenuse=\sqrt{25}\)
⇒ \(Hypotenuse=5\)
Now, r = 5
Thus by trigonometric ratio,
\(cos \theta=\frac{base}{hypotenuse}\)
⇒ \(cos \theta=\frac{3}{5}\)
Hence we can conclude that the trigonometric ratio cos θ is 3/5.
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