Question

Find the exact value of tan (arcsin (2/5)).

Answer 1

0.4364

Answer 2

@AFleming42 got it..??

Answer 3

what's the answer in terms of pi? @Kashan

Answer 4

let [arcsin(2/5)] = y
hence: siny = 2/5
now, rewriting tany in terms of siny (whose value is known), you get:

tany = siny/cosy = siny/[±√(1 - sin²y)]
owing to arcsine function range (-pi/2,+pi/2), being siny positive, y belongs to the 1st quadrant, thus cosy is positive too;
therefore, taking the plus sign,
tany = siny/√(1 - sin²y) = (2/5)/√[1 - (2/5)²]

Answer 5

= (2/5)/√[1 - (4/25)]

Answer 6

=(2/5)/√[(25-4)/25]

Answer 7

=(2/5)/√(21/25)

Answer 8

so complicated :o

Answer 9

Well It Is Not At All Complicated :(

Answer 10

Arcsin(2/5) = arcsin(y/r) ⇒
x = √(5² - 2²) = √(25 - 4) = √21 ⇒
tan(arcsin(2/5)) = y/x = 2/√21