# Components of Vectors

#### j doe

1. The problem statement, all variables and given/known data
Finn is lost in the woods, trying to find his way back home which he knows is 7.00 km at a 120.0° angle from his current location. He decides to travel 2.00 km at a 40.0° angle followed by another 5.00 km at a 100° angle.

1) What is his current location using a km coordinate plane system and assuming that (0,0) was his starting location?

2) Using information from the previous question, what new vector should Finn plot to get himself home?

2. Relevant equations

3. The attempt at a solution
1) current location: 2cos40 + 5cos100 = 0.664
2) new vector: 7cos120 - 0.664 = -4.16

can someone please explain to me why you use cosine and those specific numbers together?

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#### SteamKing

Staff Emeritus
Homework Helper
1. The problem statement, all variables and given/known data
Finn is lost in the woods, trying to find his way back home which he knows is 7.00 km at a 120.0° angle from his current location. He decides to travel 2.00 km at a 40.0° angle followed by another 5.00 km at a 100° angle.

1) What is his current location using a km coordinate plane system and assuming that (0,0) was his starting location?

2) Using information from the previous question, what new vector should Finn plot to get himself home?

2. Relevant equations

3. The attempt at a solution
1) current location: 2cos40 + 5cos100 = 0.664
2) new vector: 7cos120 - 0.664 = -4.16

can someone please explain to me why you use cosine and those specific numbers together?
Have you made a sketch of this problem? That should go a long way to showing you what these distances are.

#### FactChecker

Gold Member
2018 Award
Depending on how you measure the angles (clockwise or counter-clockwise, with 0 angle along the x or along the y axis), the cosine is one of the x,y coordinates and the sine is the other. So your calculations are only keeping track of one of the two x,y coordinates. You need similar equations with sine to keep track of the other. Also be careful about which direction is positive and which is negative.

"Components of Vectors"

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