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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".