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lucky_girl
Jul 2, 2009, 04:05 PM
Find all values for θ such that 0≤θ<2π
a. cos(θ)=1
θ=0
b. sin(θ)=0.5
θ=30,150
is this ans. Are right??
I want help in this que. Sin(θ)= π (pi)
Perito
Jul 2, 2009, 06:00 PM
a. Don't forget \theta = 2 \pi \,= \, 360\, degrees
b. for 0 \,\le\, \theta \,\le\, 2 \pi you are correct
sin(\theta)=\pi
But -1 ≤ sin(θ) ≤ 1 and π > 1. so it's not defined except as a complex number
lucky_girl
Jul 2, 2009, 08:04 PM
hey can you help me with this a.sin(θ)=1/√2
b. tan(θ)=1/2
Perito
Jul 2, 2009, 08:20 PM
a.sin(θ)=1/√2
b. tan(θ)=1/2
Sin(\theta) = \frac {1}{\sqrt {2}} = \frac {\pi}{4} = 45\,deg
\theta = ArcSin \left( \frac {1}{\sqrt {2}} \right)
Tan(\theta) = \frac 12
\theta = ArcTan \left( \frac 12 \right) = 0.148 \, \pi = 26.565\, deg
Most scientific calculators have ArcSin and ArcTan functions on them. ArcSin is "the angle whose sine is". It's also written sin^{-1}. This does not imply that
Sin^{-1}(x) \, \ne \, \frac {1}{Sin(x)}
ArcTan is the same type of thing.
You can also solve this type of problem using a "unit circle".