Find the values of theta if 0

Question

Find the values of theta if 0 <= theta <= pi ?

Sin theta = tan theta

Anna Andrews · Accepted Answer

#theta = 0, pi# # sin theta = tan theta = sin theta/cos theta # #sin theta cos theta = sin theta # #sin theta(cos theta -1 ) = 0# #sin theta = 0 or cos theta = 1# #theta = pi k or theta = 2pi k quad # integer #k# #theta = pi k# covers them both. #theta = 0, pi # in the range

Kai Anderson · Answer

undefined To find the values of $ \theta $ where $ \sin(\theta) = \tan(\theta) $ for $ 0 \leq \theta \leq \pi $, we can use the trigonometric identities:

1. $ \sin(\theta) = \frac{\sin(\theta)}{\cos(\theta)} $ (Definition of tangent)
2. $ \sin(\theta) = \frac{\sin(\theta)}{\cos(\theta)} $
3. $ \sin(\theta) \cos(\theta) = \sin(\theta) $ (Multiplying both sides by $ \cos(\theta) $)
4. $ \sin(\theta) \cos(\theta) - \sin(\theta) = 0 $
5. $ \sin(\theta)(\cos(\theta) - 1) = 0 $

This equation is true when either $ \sin(\theta) = 0 $ or $ \cos(\theta) - 1 = 0 $.

When $ \sin(\theta) = 0 $, the solutions are $ \theta = 0 $ and $ \theta = \pi $.

When $ \cos(\theta) - 1 = 0 $, we have $ \cos(\theta) = 1 $, which occurs when $ \theta = 0 $.

Thus, the solutions for $ 0 \leq \theta \leq \pi $ are $ \theta = 0 $ and $ \theta = \pi $.

Find the values of theta if 0 &lt;= theta &lt;= pi ? Sin theta = tan theta

Find the values of theta if 0 <= theta <= pi ? Sin theta = tan theta