Understanding cosine

[Paul938271849]

I’m trying to help a friend who’s doing grade 10 math, but I myself don’t know some of the parts to the equation.

The question they wish to know, is why do you bring down cos43 for the fraction near the end? We understand it’s to cancel it out, but I guess we don’t know how or why that step occurs I guess. This question may be a fraction question more then a trig question, but we are just confused how or why that step occurs, and how would you know to do that? What aren’t we understanding about that step? Thank you for any help we can get with that.

 

[Deleted member 4993]

I’m trying to help a friend who’s doing grade 10 math, but I myself don’t know some of the parts to the equation.

The question they wish to know, is why do you bring down cos43 for the fraction near the end? We understand it’s to cancel it out, but I guess we don’t know how or why that step occurs I guess. This question may be a fraction question more then a trig question, but we are just confused how or why that step occurs, and how would you know to do that? What aren’t we understanding about that step? Thank you for any help we can get with that.

The third line of the answer is incorrect (Missing something). It should have been:

Cos(43^o) \(\displaystyle \ = \ \frac{15}{x}\)

That is cos \(\displaystyle \ = \ \frac{adjacent}{hypotenuse}\)

Also remember cos(43^o) is just a number (~0.731). So you can do whatever you did with numbers.

If you have further question - please write back......

 

[Steven G]

5 = 10/2 and 2 = 10/5

7 = 21/3 and 3 = 21/7

If a = b/c then c = b/a (assuming a is not 0). That is you can interchange the a and c. Do that in Cos(43^o) = 15/x

 

[Dr.Peterson]

The question they wish to know, is why do you bring down cos43 for the fraction near the end? We understand it’s to cancel it out, but I guess we don’t know how or why that step occurs I guess. This question may be a fraction question more then a trig question, but we are just confused how or why that step occurs, and how would you know to do that? What aren’t we understanding about that step? Thank you for any help we can get with that.

They first cross-multiplied, which can be better explained as multiplying each side by x in order to cancel; then they divided both sides by cos(43) in order to leave x by itself. I think the latter is the step you're asking about.

This should be familiar with algebra problems like solving 3 = 6/x, where you can first multiply both sides by x to get 3x = 6, and then divide both sides by 3 to get x = 2. The cosine plays the role of my 3.

 

[Paul938271849]

I’m thinking we need to work on our rules of fractions. I don’t know if I can write what I’m trying to ask properly, but I guess I’m wondering, for a lack of better words, what gives you the “right” or under what rule in math gives you “permission” to just bring down that number and make it a fraction (this would of been better asked in fractions I think so my apologies for maybe posting in the wrong category). Or do I just need to accept that, that is how it is when trying to figure out cosine, that that’s just what you do?

 

[Dr.Peterson]

I’m thinking we need to work on our rules of fractions. I don’t know if I can write what I’m trying to ask properly, but I guess I’m wondering, for a lack of better words, what gives you the “right” or under what rule in math gives you “permission” to just bring down that number and make it a fraction (this would of been better asked in fractions I think so my apologies for maybe posting in the wrong category). Or do I just need to accept that, that is how it is when trying to figure out cosine, that that’s just what you do?

You don't just "bring down that number"; as I explained, you are dividing both side by that number, because dividing equal quantities by the same quantity results in equal quantities. Did you see that they wrote cos 43 under both sides, not just one, and then canceled on the left?

Ultimately this belongs under algebra, but that's okay; a lot of people studying trig (or even calculus) have difficulties that are really about learning algebra better.

So let's give you more practice. Can you show me how you would solve this equation? 6x = 15