√ 29 cos (x + 68.2° )=3.1
solve all angle of x. range is 0° to 360°
ans is 236.9° and 347.7° i think. ppls expalin to me how to do it. thank you. by the way, just afraid that it is not clear, the front part is square root 29.
√ 29 cos (x + 68.2° )=3.1
solve all angle of x. range is 0° to 360°
ans is 236.9° and 347.7° i think. ppls expalin to me how to do it. thank you. by the way, just afraid that it is not clear, the front part is square root 29.
sqrt(29) *cos(x +68.2deg) = 3.1
So,
cos(x +68.2deg) = 3.1 / sqrt(29)
cos(x +68.2deg) = 0.57566
It is a positive cosine value, so angle (x +68.2) is in the 1st and 4th quadrants.
(x +68.2deg) = arccos(0.57566) = 54.9 deg
In the 1st quadrant:
(x +68.2deg) = 54.9 deg
x = 54.9 -68.2 = -13.3 deg
That is in the 4th quadrant. If measuring by the usual counterclockwise way,
x = 360 -13.3 = 346.7 degrees ------**
In the 4th quadrant:
(x +68.2deg) = (360 -54.9) deg
x +68.2 = 305.1 deg
x = 305.1 -68.2 = 236.9 deg ------------**
Therefore, x = 236.9 deg and 346.7 deg. --------answer.
The -13.3 degrees?
It is in the 4th quadrant because it is a negative acute angle.
If it were 13.3 degrees, then it should be in the 1st quadrant because it is a positive acute angle.
Our usual direction for measuring angles is counterclockwise starting from the right branch of the horizontal axis or of the x-axis. So if an angle is negative, then it is being meaured clockwise. So -13.3 degrees is in the 4th quadrant.
The four quadrants are always "counted" counterclokwise whether the angles are measured counterclockwise or clockwise.
Another example is -95 degrees. That should be in the 3rd quadrant. And if -95 degrees is to be measured as usual....counterclockwise.... then it will be
-95 deg = (360 -95) = 265 deg. It is still in the 3rd quadrant.