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).
\(\tan\theta=\frac{y}{x}\)
\(\tan(135^{\circ})=\frac{y}{x}\)
\(\tan(90^{\circ}+45^{\circ})=\frac{y}{x}\)
Using quadrant concepts, above equation can be written as
\(-\cot(45^{\circ})=\frac{y}{x}\) \([\because \cot 45^{\circ}=1]\)
\(-1=\frac{y}{x}\) ..... (1)
In option A,
\(\frac{y}{x}=\frac{\sqrt{3}}{-1} =-\sqrt{3}
eq -1\)
In option B,
\(\frac{y}{x}=\frac{1}{-\sqrt{3}} =-\frac{1}{\sqrt{3}}
eq -1\)
In option C,
\(\frac{1}{-1}=-1\)
Therefore option C is correct.
In option B,
\(\frac{y}{x}=\frac{1}{\sqrt{3}} =\frac{1}{\sqrt{3}}
eq -1\).
Therefore correct option is C. The point on the terminal side of 135° is (-1,1).
