Question

Referring to the image below (based on vectors physics), how does he get F2X = F2Cosθ. I don't understand how he got the equation so that he knows there are equal. I circled it in orange.

Answer 1

Please see explanation below

Step-by-step explanation:

Recall that trigonometric functions like cosine (cos) and sine (sin) of an angle are defined based on the relationships between the sides and hypotenuse of a right angle triangle:

`sin(\theta)=(opposite)/(hypotenuse) \\cos(\theta)=(adjacent)/(hypotenuse)`

where the terms "opposite" and "adjacent" refer to the sides opposite and adjacent to the angle in question.

Based on such, one can solve for example for the "adjacent" side (the horizontal component of the 200 N vector you need to find) to the known angle (
`\theta`) in the following way:

`cos(\theta)=(adjacent)/(hypotenuse)\\cos(\theta)=(adjacent)/(hypotenuse)\\cos(30^o)=(adjacent)/(200)\\adjacent=200\,\,cos(30^o)`