一題f.3maths!!

1. if Sinθ=2/5，find Cosθ and Tanθ.(leave youur ansin surd form.)
Sol
Sinθ=2/5
Cos^2 θ=1－Sin^2 θ=21/25
Cosθ=+/-√21/5
(1)Cosθ=√21/5
Tanθ=2/√21=2√21/21

(2)Cosθ=－√21/5
Tanθ=-2/√21=－2√21/21

if sinθ=2/5,
we can draw a right-angled triangle
with opposite side as 2, hypotenuse as 5 then by the Pythagoras' theorem,
(the adjacent side)^2+2^2=5^2
the adjacent side =21^(1/2) cosθ
=adjacent side/hypotneuse
=[21^(1/2)]/5 tanθ
=opposite side/adjacent side
=2/[21^(1/2)]
=2*[21^(1/2)]/21