This exercise is adopted from Example 1.6-1 in Introduction to MATLAB for Engineers, third edition by William J. This matches the result of calculation: \((4)^2=(−4)^2,(−5)^2=(5)^2\), and so on. The purpose of this lab is to use MATLAB to demonstrate the use of trig functions by analyzing the movement of a piston. All along the curve, any two points with opposite x-values have the same function value. An expression can be transformed from logarithmic, trigonometric, inverse trigonometric or hyperbolic to exponentials, factorials to gamma functions. The graph of the function is symmetrical about the y-axis. As it turns out, there is an important difference among the functions in this regard.Ĭonsider the function \(f(x)=x^2\), shown in Figure. To be able to use our six trigonometric functions freely with both positive and negative angle inputs, we should examine how each function treats a negative input. Using Even and Odd Trigonometric Functions Try sind, or atan2d for the degree versions of sin. Finally, in quadrant IV, “ Class,” only cosine and its reciprocal function, secant, are positive. MATLAB conveniently defines versions of the common trig functions which take and produce values in degrees. In quadrant III, “ Trig,” only tangent and its reciprocal function, cotangent, are positive. In quadrant II, “ Smart,” only sine and its reciprocal function, cosecant, are positive. In quadrant I, which is “ A,” all of the six trigonometric functions are positive. To help us remember which of the six trigonometric functions are positive in each quadrant, we can use the mnemonic phrase “A Smart Trig Class.” Each of the four words in the phrase corresponds to one of the four quadrants, starting with quadrant I and rotating counterclockwise. Figure shows which functions are positive in which quadrant. The positive and negative signs with the trigonometric functions indicate the portion of the quadrants. The trigonometric function values for the original angle will be the same as those for the reference angle, except for the positive or negative sign, which is determined by x- and y-values in the original quadrant. Trigonometric functions show the relationship between the angles of the triangle and the lengths of its sides. The procedure is the same: Find the reference angle formed by the terminal side of the given angle with the horizontal axis. We can evaluate trigonometric functions of angles outside the first quadrant using reference angles as we have already done with the sine and cosine functions. Using Reference Angles to Evaluate Tangent, Secant, Cosecant, and Cotangent \)īecause we know the sine and cosine values for the common first-quadrant angles, we can find the other function values for those angles as well by setting x x equal to the cosine and y y equal to the sine and then using the definitions of tangent, secant, cosecant, and cotangent.
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