You can definitely transmit data using just TX & GND.
Firstly, you want to hook up the ATtiny85 TX line to the FTDI RX line (yellow on the TTL-232R). Make sure that the USB adapter can handle 5V - I'm fairly sure even the 3.3V TTL-232R is 5V tolerant.
According to the example page for SoftwareSerial, you need to set the direction of the TX & RX lines in your setup function:
// include the SoftwareSerial library so you can use its functions:
#include <SoftwareSerial.h>
#define rxPin 2
#define txPin 3
#define ledPin 13
// set up a new serial port
SoftwareSerial mySerial = SoftwareSerial(rxPin, txPin);
byte pinState = 0;
void setup() {
// define pin modes for tx, rx, led pins:
pinMode(rxPin, INPUT);
pinMode(txPin, OUTPUT);
pinMode(ledPin, OUTPUT);
// set the data rate for the SoftwareSerial port
mySerial.begin(9600);
}
The baudrate will be 4800 in your case. The SoftwareSerial library doesn't seem to support CTS & RTS, so just make sure you aren't using them on the host software.
Check out the reference page for more details, where they talk about some potential timing issues which may be exacerbated if you're running at 1MHz using the internal oscillator on the tiny.
Best Answer
The ATtiny does not have a hardware multiplier, but software multiplication is not quite as expensive as you imply. See the AVR200 application note and associated code for some optimized multiplication and division routines.
Sine and cosine calculations can be accelerated using lookup tables, effectively trading memory space for processor cycles. However, as @DaveTweed correctly pointed out, algorithmically approximating sine and cosine in software will push the cycle count up nearer the range you fear.