Mathematics For Machine Technology
8th Edition
ISBN: 9781337798310
Author: Peterson, John.
Publisher: Cengage Learning,
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Chapter 71, Problem 11A
To determine
To sketch:
A right triangle for the given angle and the sides of the triangle are to be labelled as positive or negative.
Label the sides of the triangle as positive or negative.
To find: The reference angles and functions of the angles.
The value of sine, cosine, tangent, cotangent, cosecant, secant for a given angle, up to 4 decimals.
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Chapter 71 Solutions
Mathematics For Machine Technology
Ch. 71 - Prob. 1ACh. 71 - Find the distance y to the nearest hundredth of an...Ch. 71 - Prob. 3ACh. 71 - If A = 3650', determine sin A, cos A, tan A, cot...Ch. 71 - Prob. 5ACh. 71 - Find x.Ch. 71 - For each angle, sketch a right triangle. Label the...Ch. 71 - For each angle, sketch a right triangle. Label the...Ch. 71 - Prob. 9ACh. 71 - For each angle, sketch a right triangle. Label the...
Ch. 71 - Prob. 11ACh. 71 - For each angle, sketch a right triangle. Label the...Ch. 71 - Prob. 13ACh. 71 - For each angle, sketch a right triangle. Label the...Ch. 71 - Prob. 15ACh. 71 - For each angle, sketch a right triangle. Label the...Ch. 71 - Prob. 17ACh. 71 - For each angle, sketch a right triangle. Label the...
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- 1.3. The dots of Output 2 lie in pairs. Why? What property of esin(x) gives rise to this behavior?arrow_forward1.6. By manipulating Taylor series, determine the constant C for an error expansion of (1.3) of the form wj−u' (xj) ~ Ch¼u (5) (x;), where u (5) denotes the fifth derivative. Based on this value of C and on the formula for u(5) (x) with u(x) = esin(x), determine the leading term in the expansion for w; - u'(x;) for u(x) = esin(x). (You will have to find maxε[-T,T] |u(5) (x)| numerically.) Modify Program 1 so that it plots the dashed line corresponding to this leading term rather than just N-4. This adjusted dashed line should fit the data almost perfectly. Plot the difference between the two on a log-log scale and verify that it shrinks at the rate O(h6).arrow_forwardDefine sinc(x) = sin(x)/x, except with the singularity removed. Differentiate sinc(x) once and twice.arrow_forward
- 1.4. Run Program 1 to N = 216 instead of 212. What happens to the plot of error vs. N? Why? Use the MATLAB commands tic and toc to generate a plot of approximately how the computation time depends on N. Is the dependence linear, quadratic, or cubic?arrow_forwardShow that the function f(x) = sin(x)/x has a removable singularity. What are the left and right handed limits?arrow_forward18.9. Let denote the boundary of the rectangle whose vertices are -2-2i, 2-21, 2+i and -2+i in the positive direction. Evaluate each of the following integrals: (a). 之一 dz, (b). dz, (b). COS 2 coz dz, dz (z+1) (d). z 2 +2 dz, (e). (c). (2z+1)zdz, z+ 1 (f). £, · [e² sin = + (2² + 3)²] dz. (2+3)2arrow_forward
- 18.10. Let f be analytic inside and on the unit circle 7. Show that, for 0<|z|< 1, f(E) f(E) 2πif(z) = --- d.arrow_forward18.4. Let f be analytic within and on a positively oriented closed contoury, and the point zo is not on y. Show that L f(z) (-20)2 dz = '(2) dz. 2-20arrow_forward18.9. Let denote the boundary of the rectangle whose vertices are -2-2i, 2-21,2+i and -2+i in the positive direction. Evaluate each of the following integrals: (a). rdz, (b). dz (b). COS 2 coz dz, (z+1) (d). 之一 z 2 +2 dz, (e). dz (c). (2z + 1)2dz, (2z+1) 1 (f). £, · [e² sin = + (2² + 3)²] dz. z (22+3)2arrow_forward
- 18.8. (a). Let be the contour z = e-≤0≤ traversed in the า -dz = 2xi. positive direction. Show that, for any real constant a, Lex dzarrow_forwardf(z) 18.7. Let f(z) = (e² + e³)/2. Evaluate dz, where y is any simple closed curve enclosing 0.arrow_forward18. If m n compute the gcd (a² + 1, a² + 1) in terms of a. [Hint: Let A„ = a² + 1 and show that A„|(Am - 2) if m > n.]arrow_forward
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