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

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

- ( \sin(\theta) = \frac{\sin(\theta)}{\cos(\theta)} ) (Definition of tangent)
- ( \sin(\theta) = \frac{\sin(\theta)}{\cos(\theta)} )
- ( \sin(\theta) \cos(\theta) = \sin(\theta) ) (Multiplying both sides by ( \cos(\theta) ))
- ( \sin(\theta) \cos(\theta) - \sin(\theta) = 0 )
- ( \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 ).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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