Find tanx if sinx = 3/4 and x is in quadrant II.
in Q II y is positive and x is negative
sin x = 3/4 means that y = 3, r = 4, x = -sqrt(7)
So, tan = y/x = -3/sqrt(7)
To find the value of tanx given that sinx = 3/4 in quadrant II, we can use the Pythagorean identity.
In quadrant II, the values of sinx and cosx are positive, whereas tanx is negative.
Since sinx = 3/4, we can label the opposite side as 3 and the hypotenuse as 4. We can use the Pythagorean theorem to find the adjacent side (let's call it a).
Using the Pythagorean theorem:
a^2 + 3^2 = 4^2
a^2 + 9 = 16
a^2 = 7
a = √7
Now we have the values of the opposite side (3) and the adjacent side (√7).
To find tanx, we can use the formula:
tanx = opposite/adjacent
tanx = 3/√7
To rationalize the denominator, we multiply the numerator and denominator by √7:
tanx = (3/√7) * (√7/√7)
tanx = (3√7) / 7
Therefore, the value of tanx when sinx = 3/4 and x is in quadrant II is (3√7) / 7.