Compute angles, trignometry/pre-calc?

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Homework Help Overview

The discussion revolves around a trigonometry problem involving the cosine function and the difference of sums formula. Participants are exploring the relationship between angles and their corresponding trigonometric values, particularly focusing on the implications of given values and the correct interpretation of angles in different quadrants.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are attempting to understand the difference of sums formula and its application to the problem. There is confusion regarding the interpretation of cosine values and their geometric implications. Some participants question the setup of the problem, particularly the mention of an angle π in the first quadrant.

Discussion Status

The discussion is ongoing, with participants providing insights and questioning assumptions. Some guidance has been offered regarding the use of the inverse cosine function and the need for clarification on the problem's initial conditions. Multiple interpretations of the problem setup are being explored.

Contextual Notes

There is a noted confusion regarding the initial statement of the problem, specifically the reference to an angle of π radians in the first quadrant, which some participants find contradictory. This has led to a discussion about the correct identification of angles and their quadrants.

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Homework Statement


I'm having a problem with this. I was told to use the difference of sums formula. I'm not exactly sure of what that is/means.

Homework Equations


Difference of sums?

The Attempt at a Solution


I'm thinking that Cos(a)=1/3 refers to 1 being the adjacent angle and 3 is the hypotenuse. Therefore the opposite angle equals to sqrt(32-12). Or does 1/3 somehow correspond to an angle? a or alpha should be 30 degrees then right? I need a lead-in. From there, I think that I'll be able to take it form there. Than you in advance.
 

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You are making this more complicated than necessary:

cos(a) = 1/3 = 0.3333...

Sometimes a cigar is just a cigar.
 
SteamKing said:
You are making this more complicated than necessary:

cos(a) = 1/3 = 0.3333...

Sometimes a cigar is just a cigar.

Lol, this is why I often miss a lot of points on tests, my minds always on "it's not that easy mode". But how does that go into helping me figure out the other problems(In the picture)? Being on that mode again, I'm thinking that it's not as easy as just subtracting and replacing the signs. Thank you.
 
Matriculator said:

Homework Statement


I'm having a problem with this. I was told to use the difference of sums formula. I'm not exactly sure of what that is/means.


Homework Equations


Difference of sums?


The Attempt at a Solution


I'm thinking that Cos(a)=1/3 refers to 1 being the adjacent angle and 3 is the hypotenuse. Therefore the opposite angle equals to sqrt(32-12).
No, the opposite side is sqrt(32-12). To get the opposite angle, find angle a using the inverse cosine function, and then subtract a from ##\pi##/2.
Matriculator said:
Or does 1/3 somehow correspond to an angle? a or alpha should be 30 degrees then right? I need a lead-in. From there, I think that I'll be able to take it form there. Than you in advance.
 
The beginning of the problem states:
Given an angle π in the first quadrant...
... which makes no sense. The terminal side of an angle of π radians (or 180°) would be on the negative x-axis, between the 2nd and 3rd quadrants. Do you mean to say,
"Given an angle a in the first quadrant..."?
 
eumyang said:
The beginning of the problem states:

... which makes no sense. The terminal side of an angle of π radians (or 180°) would be on the negative x-axis, between the 2nd and 3rd quadrants. Do you mean to say,
"Given an angle a in the first quadrant..."?

Yes, sorry about that. It was a stupid copy and paste of Pi, I mean a.
 
You do know the sum and difference formulas for calculating the sine and cosine of angle sums and angle differences, don't you?
 

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