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（中五數學）計算三角方程既根既問題 謝謝回答

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您好 例如 cos x = 1 / 開方2 用計數機剩係計到第一個根 = 45° 但個答案係45°同埋315° 咁315°可以點樣計出黎？唔用計數機都可以。 謝謝閣下賜教！

最佳解答:

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.

其他解答:

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.FAD2A23AB937987B