sin 450
Understand the Problem
The question is asking for the value of the sine function evaluated at 450 degrees. To solve it, we first need to consider the periodic nature of the sine function and reduce the angle accordingly.
Answer
$1$
Answer for screen readers
The value of $\sin(450^\circ)$ is $1$.
Steps to Solve
- Understanding Angle Reduction
The sine function is periodic with a period of $360^\circ$. Therefore, we can subtract $360^\circ$ from $450^\circ$ to find an equivalent angle within the range $[0^\circ, 360^\circ]$. $$ 450^\circ - 360^\circ = 90^\circ $$
- Evaluating the Sine Function
Now, we need to find the value of the sine function at the reduced angle $90^\circ$. The sine of $90^\circ$ is a well-known value: $$ \sin(90^\circ) = 1 $$
The value of $\sin(450^\circ)$ is $1$.
More Information
The sine function is widely used in trigonometry and has a periodicity of $360^\circ$. The value of $1$ for $\sin(90^\circ)$ is significant as it's the maximum value of the sine function, showing its peak at this angle.
Tips
- A common mistake is to directly calculate $\sin(450^\circ)$ without reducing the angle first. Always remember to use the periodicity of sine when dealing with angles outside the standard range.
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