Precalculus activity

Question

Find the exact values of the following under the given conditions.

a.    Sin (a+b).   b. cos (a+b).  C. tan(a+b)

b.   sina = 3/5 and a lies in quadrant I, and sinb= 5/13 and b lies in quadrant II.

Answer 1

sina=3/5 cosa =4/5

sinb = 5/13 cosb = -12/13

sin(a+b) = sinacosb + sinbcosa

= (3/5)(-12/13) + (5/13)(4/5)

= -36/65 + 20/65

sin(a+b)= -16/65

check the answer with a trig calculator

a+b = about 194.25 degrees

a= about 36.87 in quadrant I

b = about 157.38 in quadrant II

a+b = about 36.87+157.38 = 194.25 in quadrant III

cos(a+b) = cosacosb -sinasinb

= (4/5)((-12/13) - (3/5)(5/13)

= -48/65 - 3/13

= -63/65= about .97

cos194.25 = about -.97

.

tan(a+b) = sin(a+b)/cos(a+b) = 16/63 = about 0.25

tan194.25 = about 0.25