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smarty5187
24.01.2020 •
Mathematics
If cos theta = -2/3 which of the following are possible?
a. sin theta = - (sq5)/3 and tan theta = (sq5)/2
b. csc theta = 3/(sq5) and tan theta = -(sq5)/2
c. csc theta = -3/2 and tan theta = (sq5)/2
d. sin theta = (sq5)/3 and tan theta = (sq5)/2
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Ответ:
sin theta = opp/hyp = √5/3 = (sq5)/3
csc theta = 1 / sin theta = 1 / (√5/3) = 1 x 3/√5 = 3/√5 = 3/(sq5)
csc theta = 3/(sq5) and tan theta = -(sq5)/2 = B
Step-by-step explanation:
if cos theta = -2/3
the -2 is adjacent
3 is the hypothenus
using pythagoras theorem
(hypothenus)² = (opposite)² + (adjacent)²
3² = opp²+ (-2)² = opp²+ (4)
9-4 = opp² = 5
opp = √5
sin theta = opp/hyp = √5/3 = (sq5)/3
tan theta = opp/adj = √5/-2 = (sq5)/2
csc theta = 1 / sin theta = 1 / (√5/3) = 1 x 3/√5 = 3/√5 = 3/(sq5)
csc theta = 3/(sq5) and tan theta = -(sq5)/2 = b
Ответ:
t
Step-by-step explanation: