- #1
Anzas
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find the angle x
if its known that:
sin(x/2) = 1/2
tan(x)=sqrt(3)
0<=x<=360
if its known that:
sin(x/2) = 1/2
tan(x)=sqrt(3)
0<=x<=360
Solving Angle X with Sin(x/2)=1/2 & Tan(x)=sqrt(3)
- Thread starter Anzas
- Start date
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- Trigonometry
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Homework Help Overview
The discussion revolves around finding the angle x given the equations sin(x/2) = 1/2 and tan(x) = sqrt(3), with the constraint that 0 <= x <= 360 degrees. The problem involves trigonometric identities and relationships.
Discussion Character
- Exploratory, Assumption checking, Problem interpretation
Approaches and Questions Raised
- Participants explore the use of arcsine and arctangent functions but note that the intent is to utilize trigonometric identities instead. There is discussion about the potential for discovering interesting aspects of the problem and the involvement of special angles.
Discussion Status
The conversation is active, with participants sharing their thoughts on different approaches. Some have attempted to manipulate the equations but express uncertainty about how to proceed. There is a suggestion to consider the properties of an equilateral triangle as a potential avenue for exploration.
Contextual Notes
Participants are working within the constraints of the problem, specifically the requirement to avoid direct use of inverse trigonometric functions. The mention of special angles and trigonometric identities suggests that certain assumptions about the relationships between the angles may be under consideration.
- #2
Pyrrhus
Homework Helper
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why don't you simply do arcsine and arctan?
- #3
Anzas
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because the whole point of the question is using trigonometric identities to solve it (believe me i would be happy to do the arctan and get it over with 
)
)- #4
NateTG
Science Advisor
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Anzas said:because the whole point of the question is using trigonometric identities to solve it (believe me i would be happy to do the arctan and get it over with
You might discover something interesting about the problem though. (It's also worth noting that that there are special angles involved.)
- #5
Anzas
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i tried playing around with it
sin(x/2) = 1/2
tan(x)=sqrt(3)
i got
tan(x) = sin(x) / cos(x) = sqrt(3)
sin^2(x) / cos^2(x) = 3
but that didn't really lead me anywhere
i thought of ways to convert sin(x/2) to sin(x) with no luck
sin(x/2) = 1/2
tan(x)=sqrt(3)
i got
tan(x) = sin(x) / cos(x) = sqrt(3)
sin^2(x) / cos^2(x) = 3
but that didn't really lead me anywhere
i thought of ways to convert sin(x/2) to sin(x) with no luck
- #6
Tide
Science Advisor
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Anzas said:
If you don't want to use the inverse trig functions directly then you may want to ponder the equilateral triangle!
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