If sin(alpha)= 0.291 and cos(beta)=0.027 with Both angles’ terminal rays in Quadrant -1, find the values of tan(beta -alpha)

Answer 1

tan(B-A) = about -3

while A and B are both in quadrant I, A>B, so B-A <0 and in quadrant IV, where tan(B-A)<0

You could use difference formulas, sin(B-A), cos(B-A), tan(B-A)= sin(B-A)/cos(B-A)

or you could also calculate A and B, take their difference and then find the tangent.

A=about 16.9 degrees

B=about 88.45

B-A = - 71.55

tan(B-A) = -2.997 = very close to -3

You need a calculator with inverse trig functions