＊DSE Maths-Core VII: Trigonometry 三角學1

題目: sin(210'), withour calculator   (個 ' 當係degree啦...)

呢部分好重要好重要~主要有兩個steps

步驟一: 將個度數(degree)變做(0',90',180',270',360'...+/- x')
210' --> 180'+30' or 270'-60'

＊前面隻角係單數乘90'既, 個 sin變cos , cos變sin , tan變1/tan

＊前面隻角係雙數乘90'既, 個sin,cos,tan唔變
＊後面隻角照寫, 唔洗理加定減

sin(210') = sin(180'+30) -> sin30'  or

sin(210') = sin(270'-60) -> cos60' (加定減唔洗理)

步驟二: 睇下210'係邊個象限(quadrant), 跟返ASTC個野去決定正負號

210' -> 第三象限(III quadrant) -> T, tan係正數

sin210' 本身係 sin (記住係睇未變果個, 唔好睇變左果個) -> 負

so

sin(210') = sin(180'+30) = - sin30'  or

sin(210') = sin(270'-60) = - cos60' 

eg2. cos150'

cos150' = cos(180'-30') -> cos30',

150' -> II quadrant -> cos 係負 -> -cos30'

eg3. sin330'

sin330' = sin(270'+60') -> cos60'

330' -> IV quadrant -> sin 係負 -> -cos60'

eg4. tan225'

tan225' = tan(270'-45') -> 1 / tan45'

225' -> III quadrant -> tan 係正 -> + 1/ tan45'

eg5. sin(-45')

sin(-45') = sin(-90'+45') -> cos45'  (-90'當係單數(-1)乘90')

-45' -> IV quadrant -> sin 係負 -> -cos45'