find sin E and csc E if tan = 5?

Question

fustrated, HELP?

Answer 1

(sec E)^2 = (tan E)^2 + 1
sec E = sqrt( 5^2 + 1)
sec E = sqrt(26)
cos E = 1 / sec E = 1 / sqrt(26)
sin E = tan E * cos E = 5 / sqrt(26)
csc E = 1 / sin E = sqrt(26) / 5

Answer 2

It helps to understand that the tangent could be expressed TWO different ways:

opp/adj = tan E

(sin E)/(cos E) = tan E

sin E = opp/hyp

cos E = opp/hyp

In other words, you really had:

(5/hyp)/(1/hyp) = tan E

The hypotenuse canceled out, which is why you wind up with opp/adj.

You need to recreate the missing piece - namely the hypotenuse. You use the Pythagorean Theorem to do that:

1^2 + 5^2 = hyp^2
1 + 25 = hyp^2
sqrt (26) = hyp

sin E = opp/hyp, so you get:

sin E = 5/sqrt(26)

csc E = 1/(sin E) so you just flip your numerator and denominator to get the cosecant:

csc E = sqrt(26)/5

Answer 3

tan=5/1opp.side=5 and adjacent side =1
hypotenuse=(26)^1/2
sinE=5/26^1/2
cosE=1/26^1/2

Answer 4

http://en.wikipedia.org/wiki/List_of_trigonometric_identities