Cos альфа= 8/17. Найдите tg альфа

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To find tg α (tangent of α), we use the formula:

tg α = sin α / cos α

Given that cos α = 8/17, we first need to find sin α before we can find tg α.

Since sin^2 α + cos^2 α = 1, we can find sin α:

sin^2 α + (8/17)^2 = 1
sin^2 α + 64/289 = 1
sin^2 α = 1 - 64/289
sin^2 α = 225/289
sin α = √(225/289)
sin α = 15/17

Now that we have sin α, we can find tg α:

tg α = sin α / cos α
tg α = (15/17) / (8/17)
tg α = 15/8

Therefore, tg α = 15/8.