PLEASE HELP! Fill in the table below by calculating the following values of thet

Question

PLEASE HELP!

Fill in the table below by calculating the following values of theta in radians and compare them with corresponding values of sin theta and tan theta . You can evaluate sine and tangent using either value of theta , but be sure you know which mode ( degree or radian) your calculator is set to. (If you need to use infinity or - infinity , enter infinity or - infinity , respectively. ) Under what condition is the approximation sin theta tan theta theta good? The approximation is good when tan theta is greater than sin theta . The approximation is good when sin theta is greater than tan theta . The angle theta must be small, much closer to 0 degree than 90 degree . The angle theta must be large, much closer to 90 degree than 0 degree . The angle must be exactly 45 degree .

Explanation / Answer

(deg) (rad) sin tan

1 0.0174 0.0174 0.0174

2 0.0349 0.0348 0.0349

3 0.0523 0.0523 0.0524

4 0.0698 0.0697 0.0699

5 0.0872 0.0871 0.0874

10 0.1745 0.1736 0.1763

15 0.2617 0.2588 0.2679

20 0.349 0.342 0.3639

30 0.5235 0.5 0.5773

45 0.7853 0.707 1

90 1.571 1 Infinity

Now to answer the question,

as you can see in the columns for the values of angle 1,2,3,4 and 5 the value of in rads, sin and tan are approximately the same till the 3rd place of decimal.

So it is safe to assume sintan for small angles. Hence the correct answer is (C) or the 3rd option.

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