SOLUTION: Without using a calculator, find the value of t in [0,2π) that corresponds to tan (t) = 1/√3 with t in QI. Select one: a. π/6 b. 11π/6 c. 5π/6 d. 7

Algebra ->  Test -> SOLUTION: Without using a calculator, find the value of t in [0,2π) that corresponds to tan (t) = 1/√3 with t in QI. Select one: a. π/6 b. 11π/6 c. 5π/6 d. 7      Log On


   

Question 1093702: Without using a calculator, find the value of t in [0,2π) that corresponds to tan (t) = 1/√3 with t in QI.
Select one:
a. π/6
b. 11π/6
c. 5π/6
d. 7π/6
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!

you have tan(T) = 1/sqrt(3).

that means opposite leg to the angle is 1 and adjacent leg to the angle is sqrt(3).

use pythagoream formula to find hypotenuse = sqrt(1^2 + sqrt(3)^2) = sqrt(1+3) = sqrt(4) = 2.

hypotenuse is equal to 2.

that means sin(t) = 1/2.

this corresponds to an angle of 30 degrees.

tangent is positive in first quadrant and third quadrant.

angle in third quadrant is 180 + 30 = 210 degrees.

radian equivalent for 30 degrees is 30 * pi / 180 = pi/6.

radian equivalent for 210 degrees is 210 * pi / 180 = 7pi/6.

selection a and d are correct, but you want the angle in quadrant 1, so the angle has to be pi/6 which is selection a.