Question

Find the exact value of tan (arcsin (2/5)). For full credit, explain your reasoning.

Answer 1

You can see from the drawing that theta is the angle with sin 2/5. Can you now find the tangent of theta?

Answer 2

tan=opp/adj so tan(theta=2/sqrt21?

Answer 3

Yes, the tan of the angle with sin 2/5 is 2/sqrt 21

Answer 4

@Phailtacular Do you understand the reasoning?

Answer 5

With your drawing, it makes it easy, yes. But how did you determine the values? I see that sin=opp/hyp, so you were able to use 2 as the opposite side length and 5 as the hypotenuse, but how did you find sqrt22?

Answer 6

It was necessary to construct a right angled triangle with an angle having the opposite side with length 2 units and hypotenuse with length 5 units. The length of the adjacent side is found using the theorem of Pythagorus:
\[Adjacent\ side\ length=\sqrt{5^{2}-2^{2}}=\sqrt{21}\]

Answer 7

Thank you, helps a ton

Answer 8

You're welcome. BTW the answer checks out on a calculator.