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Chapter 4: Problem 83

True or False?determine whether the statement is true or false. Justify your answer. $$\frac{\sin 60^{\circ}}{\sin 30^{\circ}}=\sin 2^{\circ}$$

Short Answer

Expert verified
The statement is false.

Step by step solution

01

Evaluate the left-hand side

First, compute the fraction on the left-hand side of the equation. The sine of 60 degrees, \(\sin 60^\circ\), is equal to \(\sqrt{3}/2\), and the sine of 30 degrees, \(\sin 30^\circ\), is equal to 1/2. Substituting these in, we get \(\frac{\sin 60^\circ}{\sin 30^\circ} = \frac{\sqrt{3}/2}{1/2} = \sqrt{3}\)
02

Evaluate the right-hand side

Then, compute the right-hand side of the equation. The value of \(\sin 2^\circ\) is not standard, and it does not equal to \(\sqrt{3}\), since \(\sqrt{3}\) is the result of the larger angles and not as small as 2 degrees.
03

Compare the results

Since the computed values on both sides of the equation do not match, it's concluded that the given equation is false.

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