Question
Ch 1 Q 62 from physics for scientists and engineers 8th edition
Demonstrate that for small angles
tan alpha = sin alpha = alpha = pi(alpha')/180 degrees
where alpha is in radians and alpha' is in degrees.
(The = actually is not equal but approximately, I just don't have the approximate symbol)
Is this problem answer going to be an equation?? I'm not sure what to do with it.
For part B is says use a calculator to find the largest angle for tan alpha may be approximated by alpha with an error less than 10%
What does this mean!! help! Thanks so much in advance
Explanation / Answer
The above answer was not displayed clearly. For part A, use a calculator: alpla = 0, tan alpha = 0, sin alpha = 0 alpla = 0.05, tan alpha = 0.050042, sin alpha = 0.049979 alpla = 0.1, tan alpha = 0.10033, sin alpha = 0.099833 alpla = 0.15, tan alpha = 0.15114, sin alpha = 0.14944 alpla = 0.2, tan alpha = 0.20271, sin alpha = 0.19867 we can see that alpla (approximately) = tan alpha (approximately) = sin alpha For part B is says use a calculator to find the largest angle for tan alpha may be approximated by alpha with an error less than 10% (tan alpha - alpha)/aplha < 10% tan alpha < 1.1 alpha alpha = 0, tan alpha = 0, 1.1 alpha = 0 alpha = 0.05, tan alpha = 0.050042, 1.1 alpha = 0.055, tan alpha < 1.1 alpha alpha = 0.1, tan alpha = 0.10033, 1.1 alpha = 0.11, tan alpha < 1.1 alpha alpha = 0.15, tan alpha = 0.15114, 1.1 alpha = 0.165, tan alpha < 1.1 alpha alpha = 0.2, tan alpha = 0.20271, 1.1 alpha = 0.22, tan alpha < 1.1 alpha alpha = 0.3, tan alpha = 0.30934, 1.1 alpha = 0.33, tan alpha < 1.1 alpha alpha = 0.4, tan alpha = 0.42279, 1.1 alpha = 0.44, tan alpha < 1.1 alpha alpha = 0.5, tan alpha = 0.54630, 1.1 alpha = 0.55, tan alpha < 1.1 alpha alpha = 0.51, tan alpha = 0.55936, 1.1 alpha = 0.56100, tan alpha < 1.1 alpha alpha = 0.52, tan alpha = 0.57256, 1.1 alpha = 0.57200, tan alpha > 1.1 alpha answer: alpha = 0.52