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.

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all the angles opposite to the angle 150 would be 150 and all the angles that are next to 150 are 30 because they equal 180 it you add it up.

step-by-step explanation: