Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

$$\tan θ = 1$$ $$\sin θ = ?$$

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

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

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:

  • $\theta = \frac{\pi}{4}, \sin(θ) = \frac{\sqrt{2}}{2},$
  • $\theta = \frac{5\pi}{4}, \sin(θ) = -\frac{\sqrt{2}}{2}.$
share|cite|improve this answer
-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
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


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

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.