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

2 Answers
Dec 15, 2016

Answer:

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

Explanation:

#tanB=3#

#sinB/cosB=3#

#sinB=3cosB#

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

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

Dec 15, 2016

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!