Explain how we know that the sine of 270 degrees is -1. State one other value of θ such that sinθ=1.

Solution :

Trigonometry is that branch of mathematics which is used to study the relationship between the angles and the lengths of the sides of a triangle.

We known that the co-ordinate of a point on the circumference of a circle making an angle θ with the horizontal having a unit radius is given by :

(1 cos θ, 1 sin θ).

And for any angle made by sin θ on the x - axis is 0 and on the y -axis is 1 or -1 depending on the quadrant.

Since, angle 270 degree falls on the 3rd quadrant, therefore, the value of the co-ordinates of the point is (cos θ, sin θ) = (0,-1).

So the value of sin 270° = -1.

One other example of sin θ = 1 is 90° as 90 degree falls in the first quadrant.