Find all solutions A between 0 and 360 without a calculator:

Question

a) cos A = cos 251 b) cos A = 1.5 c) sin A = sin 251 d) cos A = cos(−110)

Answer 1

a) cosA = cos251°; A = 251° or A = 180°- (251° - 180°) = 109°.

b)cosA = 1.5; A DNE or no solutions.

c) sinA = sin251°, A = 251° or A = 360° - (251° - 180°) = 289°

d) cosA = cos(- 110°) = cos110°, A = 110° or A = 180° + (180°- 110°) = 250°

WE used Reference Angle Theorem

Answer 2

Emma

For (a), obviously A = 251 is one solution. Since on the unit circle the cosine is the x coordinate of the reference angle (251) , there will be another solution in the 2nd quadrant. A = (180 - (251-180 ) = 109.

(b) Maybe it is a typo, but cos A = 1.5 has no solution because -1 <= cos A <= +1 for all A

(c) A=251 obviously. As on the unit circle sin is the y coordinate , there will be another solution in the 4th quadrant. A = 270 + (270-251) = 289.

(d) -110 means we go clockwise from the x-axis. So a reference angle of -110 is the same as a reference angle of + 250. (360 - 110). So A=250 obviously, and second solution A = (180 - (250-180)) = 110 (USING SAME ARGUMENT AS IN (a))

Suggest you draw the angles on a unit circle to check the arguments and check the solutions are correct on a calculator.

Mike