Question

一些英文的数学题...十分着急 高手请帮忙! 谢谢!

find each value by referring to the graphs of the trigonometric function.
1. sin(-720度) 2.cos(540度) 3csc(720度)
find the values of & for which each equation is true.
1.sin & =-1 2.tan & =0
state the amplitude, period, and phase shift for each function.
1.Y=-2sin& 2.Y=-3sin 4& 3.Y=2.5cos(&+180度)
write an equation of the sine function with each amplitude, period, and phase shit.
1. amplitude=0.75, period = 360度, phase shift=30度
write an equation of the cosine function with each amplitude, period,and phase shift.
1. amplitude=3.75,period =90度, phase shift = 4度.

Answer 1

find each value by referring to the graphs of the trigonometric function.
根据(三角)函数图像，找到下列三角函数的值
1、sin(720°) = sin(0°+2*360°)= sin 0 °=0
2、cos(540°) = cos(180°+360°) = cos 180°= -1
3、csc(720°) = 1/sin(720°) = 1/sin 0 ° = ∞ No significance

find the values of & for which each equation is true.
1、sin & = -1 ，period T=360°，so & = -90°+ n*360°, n is a integer
2、tan & =0， period T=180°，so & = n*180°,n is a integer

state the amplitude(振幅), period(周期), and phase shift(相移,ω&+∮,&=0的值 ) for each function.
1、Y=-2sin& ，amplitude A= -2， period T= 360°， phase shift 为 0°
2、Y=-3sin 4& ，amplitude A= -3， period T= 90°， phase shift 为 0°
3、Y=2.5cos(&+180度)，mplitude A= 2.5， period T= 360°， phase shift 为 180°

write an equation of the sine function with each amplitude, period, and phase shit.
1. amplitude=0.75, period = 360度, phase shift=30度
0.75sin(x+30°)

write an equation of the cosine function with each amplitude, period,and phase shift.
1. amplitude=3.75,period =90度, phase shift = 4度.
3.75cos(4x+4°)

Answer 2

A：find each value by referring to the graphs of the trigonometric function.
1. sin(-720°) =0；2.cos(540°) =-1；
3. csc(720°)无意义，题目是否有错？因为csc&=1/sin&，而sin720°=0,显然csc720°无意义，除数不能为0。若是求sec720°=1=1/cos720°，cos720°=1
基本公式:sec&=1/cos&, csc&=1/sin&
B：find the values of & for which each equation is true.
1.sin & =-1 ，则&=2n*360°+270° 2.tan & =0，则&=n*180°(n is a integer)
C：state the amplitude, period, and phase shift for each function.
1.Y=-2sin& amplitude=2, period=2∏=360° (圆周率), phase shift=0
2.Y=-3sin 4& amplitude=3, period=∏/2 =90°(圆周率), phase shift=0
3.Y=2.5cos(&+180°)=-2.5cos&, amplitude=2.5, period=2∏=360° (圆周率), phase shift=0
D：write an equation of the sine function with each amplitude, period, and phase shit.
1. amplitude=0.75, period = 360°, phase shift=30°
just as, Y=0.75sin(&+30°) or Y=-0.75sin(&+30°), also can be Y=±0.75sin(&-30°)
E：write an equation of the cosine function with each amplitude, period,and phase shift.
1. amplitude=3.75,period =90°, phase shift = 4°
It can be Y=3.75cos(4& +4°) or Y=-3.75cos(4& +4°), and still be Y=±3.75cos(4& -4°)