Answer:
The correct option is C. The point on the terminal side of 135° is (-1,1).
Step-by-step explanation:
The point must be lies on the second quadrant because terminal angle is 135°.
Let the required point be (x,y).
[tex]\tan\theta=\frac{y}{x}[/tex]
[tex]\tan(135^{\circ})=\frac{y}{x}[/tex]
[tex]\tan(90^{\circ}+45^{\circ})=\frac{y}{x}[/tex]
Using quadrant concepts, above equation can be written as
[tex]-\cot(45^{\circ})=\frac{y}{x}[/tex] [tex][\because \cot 45^{\circ}=1][/tex]
[tex]-1=\frac{y}{x}[/tex] ..... (1)
In option A,
[tex]\frac{y}{x}=\frac{\sqrt{3}}{-1} =-\sqrt{3}\neq -1[/tex]
In option B,
[tex]\frac{y}{x}=\frac{1}{-\sqrt{3}} =-\frac{1}{\sqrt{3}}\neq -1[/tex]
In option C,
[tex]\frac{1}{-1}=-1[/tex]
Therefore option C is correct.
In option B,
[tex]\frac{y}{x}=\frac{1}{\sqrt{3}} =\frac{1}{\sqrt{3}}\neq -1[/tex].
Therefore correct option is C. The point on the terminal side of 135° is (-1,1).
