The points are on the graph y = tanx are [tex]\rm \left (\dfrac{4\pi }{3}, \ \sqrt{3} \right), \ and\ \left (\dfrac{\pi }{3}, \ \sqrt{3} \right )[/tex].
We have to determine
Which points are on the graph y = tan x?
Trigonometric graphs;
The graphs of trigonometric functions have the domain value of θ represented on the horizontal x-axis and the range value represented along the vertical y-axis.
For every value of the value, y is equal then check for all values of x and y.
1. The value of x is 4π/3 the value of y is;
[tex]\rm y =tanx\\\\y=tan\dfrac{4\pi }{3}\\\\y=\sqrt{3}[/tex]
2. The value of x is π/4 the value of y is;
[tex]\rm y =tanx\\\\y=tan\dfrac{\pi }{4}\\\\y=1[/tex]
3. The value of x is π/6 the value of y is;
[tex]\rm y =tanx\\\\y=tan\dfrac{\pi }{6}\\\\y=\dfrac{\sqrt{3} }{3}[/tex]
4. The value of x is π/3 the value of y is;
[tex]\rm y =tanx\\\\y=tan\dfrac{\pi }{3}\\\\y=\sqrt{3} }[/tex]
5. The value of x is 1 the value of y is;
[tex]\rm y =tanx\\\\y=tan(1)\\\\ y=\dfrac{\pi }{4}[/tex]
Hence, the points are on the graph y = tanx are [tex]\rm \left (\dfrac{4\pi }{3}, \ \sqrt{3} \right), \ and\ \left (\dfrac{\pi }{3}, \ \sqrt{3} \right )[/tex].
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