Thread: Help on triogonometry. Test tomorrow!

√ 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.

Originally Posted by helloying

√ 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.

but how did u know when to put the negative in the 4th quadrant or watever and when to reject it? i had mistaken the negative i had gotten to be out of the range so i reject the -13.3

Originally Posted by helloying

but how did u know when to put the negative in the 4th quadrant or watever and when to reject it? i had mistaken the negative i had gotten to be out of the range so i reject the -13.3

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.