Find sin θ, if cos θ = 2/5 and tan θ

Question

Find sin θ, if cos θ = 2/5 and tan θ < 0

shamim · Answer

Given
Cos theta=2/5

shamim · Answer

Need to draw a right angle triangle

shamim · Answer

Base=2
Hypotenuse=5

shamim · Answer

Pythagorean theorem
Hypotenuse^2=base^2+perpendicular^2

shamim · Answer

5^2=2^2+perpendicular^2
Perpendicular=root 21
Right?

dtan5457 · Answer

How I would go about a problem like this is...

knowing that

sin(theta)^2+cos(theta)^2=1

subsititute cos (2/5)

sin(theta)^2+(2/5)^2=1

(2/5)^2=4/25

sin^2=21/25

take square root

sin=sqrt21/5
It says that tan<0..so it's not quadrant 1 or 3, and since cos is positive, this must be the 4th quadrant and sin is negative.

dtan5457 · Answer

but if you are not familiar with identities, follow @shamim 's way

cobaltthunder267 · Answer

Oh, okay! I think I get it now!!

I'm still working on Identities, so I wasn't quite sure how to apply them. Thank you guys so much! @dtan5457 & @shamim!

dtan5457 · Answer

Alright, it's best to get familiar with both...some teachers (my teacher) forces us to use identities when asked upon...so...try and memorize them.

shamim · Answer

Welcome!!!!!