Suppose tan(x) = Two-thirds, and the terminal side of x is located in quadrant I. What is sin(x)?

sin(x) = 2/√13

Step-by-step explanation:

In the first quadrant , all the trig identity (sin, cos and tan) are all positive.

Given tan(x) = 2/3

According to TOA, tan(x) = opposite/adjacent = 2/3

opposite = 2

adjacent = 3

Using pythagoras theorem to get the hypotenuse;

Hyp² = opp²+adj²

Hyp² = 2²+3²

Hyp² = 4+9

Hyp² = 13

Hyp = √13

According to SOH, sin(x) = opp/hyp

sin(x) = 2/√13

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