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Sagot :
Answer:
B
Step-by-step explanation:
sinx = 3/5
to find the value of x...figure sine inverse(Arcsin) of 3/5 out.
sin^-1 ( 3/5) = 0.64.
siny = 7/25
sin^-1(7/25) = 0.28
x = 0.64
y = 0.28
tan(x-y)
=tan(0.64-0.28)
= tan (0.36)
= tan (9/25)
= 0.376.
now divide every fraction given from a - d to find the one equivalent to 0.376 because that's the value of tan(x-y).
B. 44 / 117 = 0.376.
Answer:
b
Step-by-step explanation:
sin x = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{3}{5}[/tex]
This is a 3- 4- 5 right triangle
with adjacent side = 4 , then
cos x = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{4}{5}[/tex] , thus
tan x = [tex]\frac{sinx}{cosx}[/tex] = [tex]\frac{\frac{3}{5} }{\frac{4}{5} }[/tex] = [tex]\frac{3}{5}[/tex] × [tex]\frac{5}{4}[/tex] = [tex]\frac{3}{4}[/tex]
---------------------------------------------------
sin y = [tex]\frac{7}{25}[/tex]
This is a 7- 24- 25 right triangle
with adjacent side = 24 , then
cos y = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{24}{25}[/tex] , thus
tan y = [tex]\frac{siny}{cosy}[/tex] = [tex]\frac{\frac{7}{25} }{\frac{24}{25} }[/tex] = [tex]\frac{7}{25}[/tex] × [tex]\frac{25}{24}[/tex] = [tex]\frac{7}{24}[/tex]
----------------------------------------------------
tan(x - y) = [tex]\frac{tanx-tany}{1+tanxtany}[/tex]
= [tex]\frac{\frac{3}{4}-\frac{7}{24} }{1+\frac{3}{4}(\frac{7}{24}) }[/tex]
= [tex]\frac{\frac{11}{24} }{1+\frac{21}{96} }[/tex]
= [tex]\frac{\frac{11}{24} }{\frac{117}{96} }[/tex]
= [tex]\frac{11}{24}[/tex] × [tex]\frac{96}{117}[/tex]
= [tex]\frac{11}{1}[/tex] × [tex]\frac{4}{117}[/tex]
= [tex]\frac{44}{117}[/tex] → b
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