Pre cal help URGENT

Question

Which of the following is a solution to 3tanθ=√3  ?

 

π/6

 

-π/2

 

π/3

 

π/2

Answer 1

Hi Naiomi, we can graph the values of each of the values and from the graphs, find out which one is the answer.

 

π/6 = 30 degrees. When we graph this, we get the y-value = 1, and the hypotenuse would be 2, or twice the y-value. We can then use the Pythagorean Theorem to find the x-value.

 

2² = 1² + x²

 

Solving for x gives x = √3

 

Then the tan π/6 = opposite side (y-value) / adjacent side (x-value) or 1 / √3

 

Removing the √3 in the denominator gives: tan π/6 = √3 / 3

 

Multiplying both sides by 3 gives: 3 tan π/6 = 3

 

You can do the same process for the other values.

 

Answer: θ = π/6

 

Questions?

Answer 2

Divide both sides of the equation by 3.

 

tanθ = √(3) / 3

 

 

Then take the inverse of tangent.

 

θ = tan^-1(√(3) / 3)

 

 

Your result will be in degrees.  You must convert them to radians, since your choices are in radians.  Lucky for you, your choices are angles on the unit circle.