（中五數學）計算三角方程既根既問題 謝謝回答

Step 1 : Make use of CAST to determine which quadrant is the other answer. For this question, it is cosine +ve, so answer is in the 1st or 4th quadrant. Answer provided by the calculator is in the 1st quadrant, so the other answer must be in the 4th quadrant.
Step 2 : Draw an angle of 45 degree ( answer from the calculator) from the x - axis.
Step 3 : Counting from 0 degree in the anti- clockwise direction to the 45 degree line will give the other answer = 360 - 45 = 315 degree.
You may try with sine, tangent, +ve and -ve to verify the steps.

2014-11-18 07:39:42 補充：
Correction : Step 2 : Draw an angle of 45 degree ( answer from the calculator) IN THE 4TH QUADRANT from the x - axis.

2014-11-18 07:40:45 補充：
Correction : Step 2 : Draw an angle of 45 degree ( answer from the calculator) IN THE 4TH QUADRANT from the x - axis.

If you do not want to draw the CAST diagram every time, you may memorise and work out via the following formulae:
sin θ= sin (180°-θ)
cos θ= cos (360°-θ)
tan θ= tan (180°+θ)

So, when 45° is a solution in the first quadrant, (180°-45°) is another solution in the unit circle.