09.Standard mathematical functions.ipynb

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    "exp10(a)"
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    "log2(a)"
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    "log1p(a)"
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    "rad2deg(a)"
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     "execution_count": 17,
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    "sin(a)"
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     "execution_count": 18,
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   "source": [
    "sind(a)"
   ]
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     "execution_count": 19,
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   "source": [
    "sind(a) # sine of a in degrees"
   ]
  },
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   "cell_type": "code",
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     "execution_count": 20,
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   "source": [
    "sinpi(a)  # sine of pi*a (more accurate than sin(pi*a)"
   ]
  },
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     "execution_count": 21,
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   "source": [
    "sinc(a)\n",
    "# (sine of pi*a)/(pi*a)"
   ]
  },
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   "cell_type": "code",
   "execution_count": 22,
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     "execution_count": 22,
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   ],
   "source": [
    "asind(1)\n",
    "# inverse sine of a in degrees"
   ]
  },
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   "cell_type": "code",
   "execution_count": 23,
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   "outputs": [
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     "execution_count": 23,
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   "source": [
    "sinh(a)\n",
    "# hyperbolic sine of a"
   ]
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   "cell_type": "code",
   "execution_count": 24,
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     "execution_count": 24,
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   "source": [
    "asinh(a)\n",
    "# inverse hyperbolic sine of a"
   ]
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   "source": [
    "cos(a) # cosine of a"
   ]
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    "tan(a)  # tangent of a"
   ]
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   "source": [
    "sec(a)"
   ]
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   "source": [
    "csc(a)"
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   "source": [
    "cot(a)"
   ]
  },
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     "execution_count": 30,
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   "source": [
    "hypot(a,2)  # hypotenuse of a and b"
   ]
  },
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   "outputs": [
    {
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      "text/plain": [
       "120"
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     },
     "execution_count": 31,
     "metadata": {},
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   "source": [
    "factorial(5)"
   ]
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  {
   "cell_type": "code",
   "execution_count": 32,
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    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 32,
     "metadata": {},
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   ],
   "source": [
    "binomial(2,5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8"
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     },
     "execution_count": 33,
     "metadata": {},
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   ],
   "source": [
    "nextpow(2,5) # next power of a equal or after b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
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     "data": {
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       "4"
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     },
     "execution_count": 34,
     "metadata": {},
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   ],
   "source": [
    "prevpow(2,4) # previous power of a equal or after b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "nextprod([4, 2], 7) # next integer equal or bigger than c that is a product of a and b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
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    {
     "data": {
      "text/plain": [
       "true"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# are 1.0 and 1.1 the same with a tolerance level of 0.1?\n",
    "isapprox(1.0, 1.1; atol = 0.2)\n",
    " # returns true"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "false"
      ]
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     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "!isapprox(1.0, 1.1; atol = 0.2)\n",
    " # returns false"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "false"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# are 1.0 and 1.1 the same with a tolerance level of 0.01?\n",
    "isapprox(1.0, 1.1; atol = 0.01)\n",
    "# returns false"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "true"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "!isapprox(1.0, 1.1; atol = 0.01)\n",
    "# returns true"
   ]
  }
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