The correct question is Use the given information to find the exact value of the expression. sin α = 21/29, α lies in quadrant II, and cos β = 15/17, β lies in quadrant I Find sin (α - β).
we know that sin(α − β<span>) = </span>sin α cos β − cos α sin β
α lies in quadrant II so cos α is negative sin α is positive
β lies in quadrant I so cos β is positive sin β is positive
step 1 find sin β cos β=15/17 sin² β+cos² β=1-----------> sin² β=1-cos² β----> sin² β=1-(15/17)² sin² β=1-225/289-----> 64/289 sin β=8/17
step 2 find cos α sin α = 21/29 cos² α + sin² α=1----> cos² α=1-sin² α---> cos² α=1-(21/29)²---> 1-441/841 cos² α=400/841------> cos α=-20/29 (remember cos α is negative)
step 3 find sin(α − β) sin α = 21/29 cos α=-20/29 sin β=8/17 cos β=15/17
Answer: The answer for this question would be answer choice B "(0, 10) and (1, 15)". (0, 10) represents her starting amount and week saved, and (1, 15) would represent her saving for one week and having $15 total.
