Question

Sin400°=

1. sin40°
2. -sin40°
3. sin(-40)°

Answer 1

sin(40°)

Explanation:

Trigonometric functions such as sine, cosine, tangent whose short forms are sin, cos, tan respectively are repetitive functions which repeat itself after every integral multiple of 2π radian or 360°. It means if you add or subtract 360° from any input of trigonometric function the output of the function won't change.

It means sin(θ) = sin(θ - n×360°) = sin(θ + n×360°)

similarly cos(θ) = cos(θ - n×360°) = cos(θ + n×360°)

and tan(θ) = tan(θ - n×360°) = tan(θ + n×360°)

where n is an integer.

So, by this sin(400°) = sin(400° - 360°) = sin(40°)