Exact values of sin(30) and cos(3pi/2)

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To find exact values for trigonometric functions like sin(30) and cos(3pi/2), use trigonometric identities for simple expressions. For more complex functions, apply series expansions such as Taylor or Euler's. The exact value of sin(30) is 1/2, while cos(3pi/2) equals 0. Drawing a triangle can help visualize these values in radical form. Understanding these methods allows for accurate calculations without a calculator.
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How can I work out exact values for trig functions like sin(30) and cos(3pi/2)?
 
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For simple expressions, use trigonometric/complex identities to reduce to terms you already know. For more complicated expressions, use series, ie., Taylor or Euler's expansions.
 
cscott said:
How can I work out exact values for trig functions like sin(30) and cos(3pi/2)?

Like the decimal values? Without a calculator?

I would just draw out the triangle and leave the answer in the exact radical form, like in your first example. But \cos{\frac{3\pi}{2}} is 0 so that should be easy.
 
Ah thanks.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

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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