What is sin 45 degrees in fraction?
Understand the Problem
The question is asking for the sine of 45 degrees expressed as a fraction, which is a trigonometric concept.
Answer
\(\frac{\sqrt{2}}{2}\)
Answer for screen readers
The sine of 45 degrees expressed as a fraction is (\frac{\sqrt{2}}{2})
Steps to Solve
-
Convert degrees to radians (optional)
Often, trigonometric functions are given in radians. To convert from degrees to radians, you can use the formula: $$ \text{radians} = \text{degrees} \times \frac{\pi}{180} $$
However, in this case, it is known that the sine of 45 degrees has a standard value that can be memorized.
- Use the standard trigonometric value
The sine of 45 degrees (or (\frac{\pi}{4}) radians) is known to equal (\frac{\sqrt{2}}{2}). Hence: $$ \sin(45^{\circ}) = \frac{\sqrt{2}}{2} $$
Therefore, we have: $$ \sin(45^{\circ}) = \frac{1}{\sqrt{2}} $$
- Rationalize the denominator (optional)
This step is optional but often done for clarity. To rationalize the denominator: Multiply the numerator and the denominator by (\sqrt{2}): $$ \sin(45^{\circ}) = \frac{1}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}} = \frac{\sqrt{2}}{2} $$
The sine of 45 degrees expressed as a fraction is (\frac{\sqrt{2}}{2})
More Information
This value is one of the standard trigonometric values which are used frequently in many areas of math and physics.
Tips
A common mistake is forgetting to rationalize the denominator. While (\frac{1}{\sqrt{2}}) is correct, (\frac{\sqrt{2}}{2}) is the preferred form.
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