How does rheumatoid arthritis cause tachycardia?

Rarely. The pain of the joints and tendon are more likely to cause tachycardia then RA directly.
Rheumatoid arthritis. Ra may cause rapid heart rate(hr) in a variety of ways. People with RA are often anemic because of chronic inflammation, the hr increases to deliver adequate oxygen. Inflamed joints lead to less exercise & deconditioning increases the hr. Ra can attack either the heart or lungs and increase the heart rate, RA is a systemic illness and affects organs other than the joints.