Evaluate sin(1/2) + cos(1)
Understand the Problem
The question requires evaluating the expression sin(1/2) + cos(1). This involves calculating the sine of 0.5 radians and the cosine of 1 radian, then summing the two values. These are trigonometric functions and will require a calculator.
Answer
$\sin(1/2) + \cos(1) \approx 1.0197$
Answer for screen readers
$ \sin(1/2) + \cos(1) \approx 1.0197 $
Steps to Solve
- Calculate sin(1/2)
Make sure your calculator is in radian mode. $$ \sin(0.5) \approx 0.4794 $$
- Calculate cos(1)
Make sure your calculator is in radian mode. $$ \cos(1) \approx 0.5403 $$
- Add the results
Add the values obtained in the previous steps. $$ \sin(0.5) + \cos(1) \approx 0.4794 + 0.5403 = 1.0197 $$
$ \sin(1/2) + \cos(1) \approx 1.0197 $
More Information
The sine and cosine functions are periodic, oscillating between -1 and 1. When evaluating trigonometric functions, it is important to ensure your calculator is in the correct mode (degrees or radians). The argument to the sine and cosine functions are in radians in this question as there is no degree symbol.
Tips
A common mistake is forgetting to set your calculator to radian mode when evaluating $ \sin(0.5) $ and $ \cos(1) $. If your calculator is in degree mode, you will get incorrect results. For example, $ \sin(0.5^{\circ}) $ is approximately 0.0087 and $ \cos(1^{\circ}) $ is approximately 0.9998.
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