- #1
ProBasket
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tan(theta) + tan(theta) is equal to tan(2theta) right? just want to make sure
Quick Math: Is tan(theta) + tan(theta) equal to tan(2theta)?
- Thread starter ProBasket
- Start date
AI Thread Summary
tan(theta) + tan(theta) equals 2tan(theta), not tan(2theta). The correct formula for tan(2theta) is 2tan(theta)/(1-tan^2(theta)). Some users initially confused the addition of two tangent values with the tangent of a double angle. The discussion also touched on the ability to factor out constants in integrals, confirming that 2 can be taken out of the integral of tan(theta). Overall, the thread clarifies the misunderstanding around the tangent addition and double angle formulas.
- #2
learningphysics
Homework Helper
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ProBasket said:
No. tan(theta) + tan(theta) is just 2tan(theta).
tan(2theta)=2tan(theta)/(1-tan^2(theta))
- #3
vincentchan
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NO...
tan \theta + tan \theta = 2 tan \theta = tan 2 \theta ( 1-tan^2 \theta)
tan \theta + tan \theta = 2 tan \theta = tan 2 \theta ( 1-tan^2 \theta)
- #4
ProBasket
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yea first i thought that tan(theta) + tan(theta) was 2tan(theta), but it didnt make sense for some reason cause it's 2*tan(theta), if you did a integral, can you take out the 2? to look like 2\int tan(theta)
maybe I'm thinking too much, cause it's really really late right now, well I'm going to get some sleep. thanks for the help
maybe I'm thinking too much, cause it's really really late right now, well I'm going to get some sleep. thanks for the help
Last edited:
- #5
Nylex
- 552
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ProBasket said:
Yes and what you have is 1*tan (theta) + 1*tan (theta).
An integral. Yes you can take the 2 out. You missed the d(theta) as well
.
Neglect gravity other than that of water; neglect friction.
F1=ρgsh=1000*10*1*(1+4)=50000 N;
F1=ρgsh=1000*10*0.1*4=4000 N;
F3=50000-4000=46000 N?
TL;DR Summary: I came across this question from a Sri Lankan A-level textbook.
Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water.
I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system
$$M(t) = M_{C} + m(t)$$
$$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$
$$P_i = Mv + u \, dm$$
$$P_f = (M + dm)(v + dv)$$
$$\Delta P = M \, dv + (v - u) \, dm$$
$$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$
$$F = u \frac{dm}{dt} = \rho A u^2$$
from conservation of momentum , the cannon recoils with the same force which it applies.
$$\quad \frac{dm}{dt}...
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