- #1
SrEstroncio
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Homework Statement
Prove [itex] \sin{10} [/itex], in degrees, is irrational.
Homework Equations
None, got the problem as is.
The Attempt at a Solution
Im kinda lost.
SrEstroncio said:Homework Statement
Prove [itex] \sin{10} [/itex], in degrees, is irrational.
Homework Equations
None, got the problem as is.
The Attempt at a Solution
Im kinda lost.
SrEstroncio said:Homework Statement
Prove [itex] \sin{10} [/itex], in degrees, is irrational.
Homework Equations
None, got the problem as is.
The Attempt at a Solution
Im kinda lost.
SrEstroncio said:I should suppose sin(10) is rational, if i am to contradict the statement, shouldn't i?
An irrational number is a real number that cannot be represented as a ratio of two integers. This means that it cannot be written as a fraction with a non-zero denominator.
The proof that sin(10) is irrational is based on the fact that if a number is a rational number, then its sine must also be a rational number. However, since sin(10) is not a rational number, it follows that it is irrational.
Proving that sin(10) is irrational is important because it helps to deepen our understanding of the properties of irrational numbers and their relationship with other mathematical concepts. It also has implications in other fields, such as physics and engineering, where trigonometric functions are used.
Yes, there is a general method for proving the irrationality of trigonometric functions. This method is based on the fact that if a trigonometric function is rational, then its argument (in this case, 10) must also be rational. By showing that the argument is irrational, we can prove that the trigonometric function is also irrational.
Yes, the irrationality of sin(10) can be proven using only elementary mathematics. The proof involves basic concepts such as the definition of an irrational number, the properties of rational and irrational numbers, and the trigonometric identities for sin(2x) and sin(5x). It does not require advanced mathematical concepts or techniques.