Question

Choose the point on the terminal side of 135°.

A. (-1, sqrt 3)
B. (-sqrt 3, 1)
C. (-1, 1)
D. (sqrt 3, -1)

Answer 1

Correct answer is C. (-1, 1)

Hope it helps

Answer 2

The correct option is C. The point on the terminal side of 135° is (-1,1).

Explanation:

The point must be lies on the second quadrant because terminal angle is 135°.

Let the required point be (x,y).

`\tan\theta=(y)/(x)`

`\tan(135^(\circ))=(y)/(x)`

`\tan(90^(\circ)+45^(\circ))=(y)/(x)`

Using quadrant concepts, above equation can be written as

`-\cot(45^(\circ))=(y)/(x)`
`[\because \cot 45^(\circ)=1]`

`-1=(y)/(x)` ..... (1)

In option A,

`(y)/(x)=(√(3))/(-1) =-√(3)\\eq -1`

In option B,

`(y)/(x)=(1)/(-√(3)) =-(1)/(√(3))\\eq -1`

In option C,

`(1)/(-1)=-1`

Therefore option C is correct.

In option B,

`(y)/(x)=(1)/(√(3)) =(1)/(√(3))\\eq -1`.

Therefore correct option is C. The point on the terminal side of 135° is (-1,1).