Find the value of tan theta if sin theta = 12/13 and theta is in quadrant 2

tanΘ = -

Step-by-step explanation:

Using the trigonometric identities

• sin²x + cos²x = 1, hence

cosx = ± √(1 - sin²x )

• tanx =

given sinΘ = , then

cosΘ = ±  

Since Θ is in the second quadrant where cosΘ < 0, then

cosΘ = -

         = - = -

tanΘ =

        = × - = -

a negative exponent is translated as follows:

so, we have

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.