How many degrees are in 2.3 clockwise rotations? What is the closests approximation for angle θ, given tan θ = 0.43?
One rotation is equal to 360 degrees. The direction (clockwise or counterclockwise) makes no difference in this case.
If we represent this as an algebraic unknown,
degrees = 2.3rotations
1 rotation = 360 degrees
degrees = 2.3(360)
This is the total number of degrees that have been completed in a rotation; we also know that we are .3 rotations away from our "degree of origin"
.3(360) = 108 degrees.
This is like saying that, if we started at the 12 o'clock position, 2.3 rotations would make two complete rotations, and then finish halfway between the 3 and 4 o'clock position.
We know that the tangent is a ratio: the relationship between one side and another. This ratio is fixed for one angle regardless of the size of the triangle. We need to know the inverse tangent in order to find the angle. The inverse trig functions show up on your calculator as `(tan^-1)`
The inverse tangent of 0.43 = 23.267
Since we're limited to 2 significant figures;
θ = 23