Evaluate the following, rounding to the nearest hundredth: sin(42°), cos(42°), tan(42°)
Understand the Problem
The question requires us to evaluate the sine, cosine, and tangent of 42 degrees. The answers should be provided as integers or decimals rounded to the nearest hundredth.
Answer
$\sin(42^\circ) = 0.67$ $\cos(42^\circ) = 0.74$ $\tan(42^\circ) = 0.90$
Answer for screen readers
$\sin(42^\circ) = 0.67$ $\cos(42^\circ) = 0.74$ $\tan(42^\circ) = 0.90$
Steps to Solve
- Find the sine of 42 degrees
Using a calculator, find the value of $\sin(42^\circ)$. $\sin(42^\circ) \approx 0.66913$
Round this value to the nearest hundredth, which is two decimal places. $\sin(42^\circ) \approx 0.67$
- Find the cosine of 42 degrees
Using a calculator, find the value of $\cos(42^\circ)$. $\cos(42^\circ) \approx 0.74314$
Round this value to the nearest hundredth, which is two decimal places. $\cos(42^\circ) \approx 0.74$
- Find the tangent of 42 degrees
Using a calculator, find the value of $\tan(42^\circ)$. $\tan(42^\circ) \approx 0.90040$
Round this value to the nearest hundredth, which is two decimal places. $\tan(42^\circ) \approx 0.90$
$\sin(42^\circ) = 0.67$ $\cos(42^\circ) = 0.74$ $\tan(42^\circ) = 0.90$
More Information
The values of sine, cosine, and tangent for angles are fundamental in trigonometry and are used extensively in fields like physics, engineering, and navigation.
Tips
A common mistake is not rounding to the correct number of decimal places as requested in the question. In this case, it is important to round to the nearest hundredth (two decimal places). Another common mistake is making sure your calculator is in degree mode, not radian mode.
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