### 2.83 How to apply a function to two lists are the same time, but with change to entries?

2.83.1 example 1
2.83.2 example 2

#### 2.83.1 example 1

Given list $$a = \{1,2,3,4\}$$ and list $$b=\{5,6,7,8\}$$ how to to call function $$f(x,y)$$ by taking $$\sin (x),\cos (y)$$ from $$a,b$$ one a time so that the result gives $f(\sin (1),\cos (5)),f(\sin (2),\cos (6)),f(\sin (3),\cos (7)),f(\sin (4),\cos (8))$

Mathematica

Remove["Global*"]
a = {1, 2, 3, 4};
b = {5, 6, 7, 8};



{f[Sin[1], Cos[5]], f[Sin[2], Cos[6]], f[Sin[3], Cos[7]], f[Sin[4], Cos[8]]}

Maple

restart;
a:=[1,2,3,4];
b:=[5,6,7,8];
f~(sin~(a),cos~(b))



[f(sin(1), cos(5)), f(sin(2), cos(6)), f(sin(3), cos(7)), f(sin(4), cos(8))]

#### 2.83.2 example 2

Given list $$a = \{1,2,3,4\}$$ and list $$b=\{5,6,7,8\}$$ how to to call function $$f(2 x+x^2+\sin (x),2+\cos (y))$$ by taking $$x,y$$ from $$a,b$$ one a time so that the result gives $\{f(3+\sin (1),5+\cos (5)),f(8+\sin (2),6+\cos (6)),f(15+\sin (3),7+\cos (7)),f(24+\sin (4),8+\cos (8))\}$

Mathematica

Remove["Global*"]
a = {1, 2, 3, 4};
b = {5, 6, 7, 8};
MapThread[f[2*#1 + #1^2 + Sin[#1], #2 + Cos[#2]] &, {a, b}]



{f[3+Sin[1],5+Cos[5]],f[8+Sin[2],6+Cos[6]],f[15+Sin[3],7+Cos[7]],f[24+Sin[4],8+Cos[8]]}

Maple

In Maple, since it does not have slot numbers # to use, it is better to make a function on the ﬂy, which does the exact same thing.

restart;
a:=[1,2,3,4];
b:=[5,6,7,8];

f~( (x->2*x+x^2+sin(x))~(a), (x->2+cos(x)) ~(b))



[f(3 + sin(1), 2 + cos(5)), f(8 + sin(2), 2 + cos(6)), f(15 + sin(3), 2 + cos(7)), f(24 + sin(4), 2 + cos(8))]