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Chapter 4: Problem 68

Verify that \(\sin \left(t_{1}+t_{2}\right) \neq \sin t_{1}+\sin t_{2}\) by approximating \(\sin 0.25, \sin 0.75,\) and \(\sin 1\).

Short Answer

Expert verified
Upon calculation, it's seen that sin(t1+t2) is not equal to sin(t1) + sin(t2), even using approximations. So, the statement was verified to be true.

Step by step solution

01

Calculate Individual Sine Values

First, we need to compute the sine values for 0.25, 0.75 , and 1. You can do this using a calculator, in radians.
02

Apply Addition Formula on Left Hand Side

Now, plug in the values of t1 and t2 into the left side of the equation, which is sin(t1+t2). Here, we assumed t1 is 0.25 and t2 is 0.75, hence calculate sin(0.25+0.75).
03

Sum up Sine Values on Right Hand Side

Then we add the sine values of t1 and t2 for the right side of the equation, which is sin(t1)+sin(t2). That will be sin(0.25) + sin(0.75).
04

Compare Both Sides

Now we compare the value we got in step 2: sin(t1+t2) with the value we got in step 3: sin(t1) + sin(t2).

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