List all points on the graph of y=tanx on the interval [π/2,3π] that have a y-coordinate of -1/radical3
(Type ordered pair)
Please teach me and show step by step work so i can learn. Thank you.
well, you know that
tan π/6 = 1/√3
using that as your reference angle, and knowing that for a triangle in standard position tan(u) = y/x, you must have either
-1/√3 (QII)
or
1/-√3 (QIV)
So, for the given domain, that means the solutions are
x = 5π/6, 11π/6, 17π/6
Thank you steve. I understand. But, in the direction, it said to type ordered pair. So how am i suppose to know what y is?.
Did you not read the problem?
points on the graph of y=tanx on the interval [π/2,3π] that have a y-coordinate of -1/radical3
geez! y = -1/√3 !!
at each of those points. So, knowing the x values, the pairs are
(5π/6,-1/√3), ...
To find the points on the graph of y = tanx on the interval [π/2, 3π] with a y-coordinate of -1/√3, we need to find the x-values that correspond to this y-coordinate.
The general equation for tanx is y = tanx. Given that we need a y-coordinate of -1/√3, we can set up the equation:
-1/√3 = tanx
To solve for x, we can take the inverse tangent (also called arctan or tan^(-1)) of both sides of the equation:
arctan(-1/√3) = arctan(tanx)
Now we need to evaluate the arctan(-1/√3).
Using a calculator in radian mode, enter -1/√3 and find its arctan value.
The result is approximately -π/6.
So, we have found one value of x, which is -π/6. However, we need to find all the other values on the interval [π/2, 3π] that also have a y-coordinate of -1/√3.
To find the other values, we can add or subtract multiples of π to the initial value -π/6.
Adding multiples of π: -π/6 + π = 5π/6, -π/6 + 2π = 11π/6, -π/6 + 3π = 17π/6
Subtracting multiples of π: -π/6 - π = -7π/6, -π/6 - 2π = -13π/6, -π/6 - 3π = -19π/6
The values of x that correspond to a y-coordinate of -1/√3 are -π/6, 5π/6, 11π/6, -7π/6, -13π/6, and -19π/6.
So, the corresponding ordered pairs are:
(-π/6, -1/√3)
(5π/6, -1/√3)
(11π/6, -1/√3)
(-7π/6, -1/√3)
(-13π/6, -1/√3)
(-19π/6, -1/√3)
These are the points on the graph of y = tanx on the interval [π/2, 3π] with a y-coordinate of -1/√3.