melanie687
28.01.2020 •
Mathematics
Find sin(a+b) if cos(a)=3/5, sin(b)= -4/5, a is in quadrant 1 and b is in quadrant 3.
cos^-1(cos(a)=3/5)cos^-1 => a = 53.13010235. sin-1(sin(b)= -4/5) => -53.13010235
a + b = 0, and sin(0) = 0. but my answer of 0 is marked wrong. what am i missing?
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Ответ:
only for . The angle you found lies in quadrant 4, not 3. Subtract 90 degrees from the angle you found and you get an angle in quadrant 3 whose sine is still -4/5, so that
or equivalently about 216 degrees (which does lie in quadrant 3).
###
Without looking for the exact values of and , we can make two observations:
is in quadrant 1, so we know and are both positive, and is in quadrant 3, so we know and are both negativeNext, we find the values of and from the given values using the Pythagorean identity:
Then using the angle sum identity for sine, we get
Ответ: