Answer: 0, π, 2π
Nevertheless, that is not an option. I see two possibilities: 1) the options are misswirtten, 2) the domain is not well defined.
If the domain were 0 ≤ θ < 2π, then 2π were excluded of the domain ant the answer would be 0, π.
Explanation:
1) The first solution, θ = 0 is trivial:
sin (0) - tan (0) = 0
0 - 0 = 0
2) For other solutions, work the expression:
sin(θ) + tan (-θ) = 0 ← given
sin (θ) - tan(θ) = 0 ← tan (-θ) = tan(θ)
sin(θ) - sin (θ) / cos(θ) = 0 ← tan(θ) = sin(θ) / cos(θ)
sin (θ) [1 - 1/cos(θ)] = 0 ← common factor sin(θ)
⇒ Any of the two factors can be 0
⇒ sin (θ) = 0 or (1 - 1 / cos(θ) = 0,
sin(θ) = 0 ⇒ θ = 0, π, 2π
1 - 1/cos(θ) = 0 ⇒ 1/cos(θ) = 1 ⇒ cos(θ) = 1 ⇒ θ = 0, 2π
⇒ Solutions are 0, π, and 2π
In fact if you test with any of those values the equation is checked. The only way to exclude one of those solutions is changing the domain.
Vsphere=(4/3)pi times r^3
r=radius
given that r=2
v=(4/3)pi2^3
v=(4/3)pi8
v=32/3pi cubic inches
about 10.66666pi cubic inches or hmm, roughly 31 cubic inches (guestimated in head)
700/200=7/2 because devide by 100 and then=3 1/2 and half is .5 so=
3.5
So decrease is 375-250=75
so convert 75/375 to percent
percent means part out of 100 so
x/100=x%
divide 125/375=0.3333/1
multiply by 100/100=33/100=33%
the answer is 33% or B
