If #tanB=3# what is #sinB#?

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Answer 1 · 2016-12-15T22:29:33

Assuming you want your answer without the use of a calculator, #sinB=3cosB#

#tanB=3#

#sinB/cosB=3#

#sinB=3cosB#

But #cosB=1/(sqrt(1+tan^2B))=1/sqrt10#

#sinB=3/sqrt10=3/10sqrt10#

Answer 2 · 2016-12-15T22:51:17

We know that #tantheta = ("side opposite "theta)/("side adjacent "theta)#

So, the side opposite #B# measures #3# and the side adjacent #B# measures #1#.

We now find the length of the hypotenuse of the imaginary triangle:

#3^2 + 1^2 = h^2#

#9 + 1 = h^2#

#h = sqrt10#

We now apply the definition that #sintheta = ("side opposite "theta)/("hypotenuse")#.

Therefore, #sintheta = 3/sqrt(10) = (3sqrt(10))/10#.

Hopefully this helps!