Bash NMR Ernst Angle Calculator

#!/bin/bash
_pi=$(echo "scale=12;4*a(1)"|bc -l)
_d1=0
_at=0
_tr=$_at+$_d1
_t1=0
_angle=0
_pw90=1
_pw=0
clear;echo
function pwToAngle {
    echo "scale=2;90*$1/$_pw90"|bc -l
}
function AngleTopw {
    echo "scale=2;$_pw90*$1/90"|bc -l
}
echo " Ernst Angle Calculator"
echo "------------------------"
echo " 1. Angle"
echo " 2. T1"
echo " 3. Recycle Delay (d1)"
echo " 4. Acq. Time (at)"
echo " 5. d1 + at"
echo
read -p "Solve for?: " response
case "$response" in
1)  read -p "Enter at (s): " _at
    read -p "Enter d1 (s): " _d1
    read -p "Enter T1 (s): " _t1
    read -p "Enter pw90 (us): " _pw90
    _ans=$(echo "e(-($_at+$_d1)/$_t1)"|bc -l)
    _ans=$(echo "a(sqrt(1-$_ans^2)/$_ans)"|bc -l)
    _ans=$(echo "$_ans*180/$_pi"|bc -l)
    _pw=$(AngleTopw $_ans)
    echo;echo "Angle = $_ans degrees ($_pw microseconds)";echo

    ;;
2)  read -p "Enter angle in degrees (or 's' for pw): " _angle
    if [ "$_angle" == "s" ]; then
        read -p "Enter pw (us): " _angle
        read -p "Enter pw90 (us): " _pw90
        _angle=$(pwToAngle $_angle)
    fi
    read -p "Enter d1 (s): " _d1
    read -p "Enter at (s): " _at
    _angleR=$(echo "$_angle*$_pi/180"|bc -l)
    _ans=$(echo "-($_at+$_d1)/l(c($_angleR))"|bc -l)
    echo;echo "T1 = $_ans seconds";echo
    ;;
3)  read -p "Enter angle in degrees (or 's' for pw): " _angle
    if [ "$_angle" == "s" ]; then
        read -p "Enter pw (us): " _angle
        read -p "Enter pw90 (us): " _pw90
        _angle=$(pwToAngle $_angle)
    fi
    read -p "Enter at (s): " _at
    read -p "Enter t1 (s): " _t1
    _angleR=$(echo "$_angle*$_pi/180"|bc -l)
    _ans=$(echo "(-l(c($_angleR))*$_t1)-$_at"|bc -l)
    echo;echo "d1 = $_ans seconds";echo
    ;;
4)  read -p "Enter angle in degrees (or 's' for pw): " _angle
    if [ "$_angle" == "s" ]; then
        read -p "Enter pw (us): " _angle
        read -p "Enter pw90 (us): " _pw90
        _angle=$(pwToAngle $_angle)
    fi
    read -p "Enter d1 (s): " _d1
    read -p "Enter t1 (s): " _t1
    _angleR=$(echo "$_angle*$_pi/180"|bc -l)
    _ans=$(echo "(-l(c($_angleR))*$_t1)-$_d1"|bc -l)
    echo;echo "at = $_ans seconds";echo
    ;;
5)  read -p "Enter angle in degrees (or 's' for pw): " _angle
    if [ "$_angle" == "s" ]; then
        read -p "Enter pw (us): " _angle
        read -p "Enter pw90 (us): " _pw90
        _angle=$(pwToAngle $_angle)
    fi
    read -p "Enter t1 (s): " _t1
    _angleR=$(echo "$_angle*$_pi/180"|bc -l)
    _ans=$(echo "(-l(c($_angleR))*$_t1)"|bc -l)
    echo;echo "at+d1 = $_ans seconds";echo
    ;;
esac