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$$\tan θ = 1$$ $$\sin θ = ?$$

Please if anyone could help with this it would be much appreciated.

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Hint: $\sin^2 x + \cos^2 x = 1$ and $ \tan x = \frac{\sin x}{\cos x}$ –  Thomas Aug 14 '13 at 13:31

2 Answers 2

Here you go:

  • $1 = \frac{\sin(θ)}{\cos(θ)}$
  • $\sin(θ) = \cos(θ)$

Using the unit circle, one can then see there are two points at which this is valid (between $0$ and $2\pi$), namely:

  • $\theta = \frac{\pi}{4}, \sin(θ) = \frac{\sqrt{2}}{2},$
  • $\theta = \frac{5\pi}{4}, \sin(θ) = -\frac{\sqrt{2}}{2}.$
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-1 for the rude "if you don't, go learn it!". I upvote the answer if the sentence is canceled. –  Avitus Aug 14 '13 at 14:35
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I'll change it! I meant it to be more in a constructive, "I used to have this same problem, but then my favorite math teacher helped me to learn the unit circle and it has really helped me", but I see what you mean, will do. –  Afrenett Aug 14 '13 at 14:37

Hints:

$$1=\tan\theta=\frac{\sin\theta}{\cos\theta}\iff \sin\theta=\cos\theta\ldots$$

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