Show:
Trigonometric
solve the Trigonometric
Proof the Trigonometric
Translation
Knowledge
Trigonometric functions of basic information
100
sin(π-x)=sinx is odd function.
What is sin(π-x)? even or odd function?
100
sin(π-x)=-sinx
what is the sin(π-x)=?
100
tanxcosx= (sinx/cosx)*cosx =sinx*cosx/cosx =sinx
What is sinx=tanxcosx how to proof?
100
(x/k+d,ay+c)
What is (x,y), translation point?
100
sinx=y/r cosx=x/r tanx=y/x
What is sinx=? cosx=? tanx=? The long is x, high is y, to the side is r.
200
cos(2π-x)=-sinx tan(2π-x)=cosx sin(2π-x)=-tanx
What is principal angle in quadrantIV? sin(π-x)=? cos(2π-x)=? tan(2π-x)=?
200
tan(π/4+π)=1
What is tan(π/4+π)=?
200
sinxcotx=sinx*(cosx/sinx) =sinx*cosx/sinx =cosx
What is sinx cotx = cosx? how to proof?
200
2π/3
What is y=3sin(3(x+π/6))-1 the period?
200
sin30=π/2 cos90=0 tan45=1
What is sin30=? cos90=? tan45=?
300
tan7π/12=tan -5π/12=-2-root3
What is tan 7π/12=? tan -5π/12=? what is they relationship?
300
tan^2x-sin^2x=sin^2x/cos^2x - sin^2x =sin^2x(1/cos^2x -1) =sin^2x (sec^2x-1) =sin^2x tan^2x
What is tan^2x- sin^2x=sin^2x tan^2x how to proof?
300
a=max-min/2
How to find the a? For example a=?
300
cscx=1/sinx secx=1/cosx cotx=1/tanx
What is csc=? sec=? cot=?
400
cot(π/2-x)=tanx
What is cot(π/2-x）=？
400
sin75°=root2+root6/4 cos105°=root2-root6/4
What is sin75°=？cos105°=？
400
cos(π/2-x) =cosπ/2 cosx+sinπ/2 sinx =(0)cosx +1 sinx =sinx
What is sinx=cos(π/2-x) how to proof?
400
a is vertical stretch or compression k is horizontal strecth or compression d is horizontal translation c is vertical translation
What is a sin k (x-d)+c a,k,d,c the meaning?
400
In quadrant 1, All ratios are positive. In quadrant 2, only sine is positive. In quadrant 3, only Tangent is positive. In quadrant 4, only Cosine is positive.
What is the quadrant 1 what is the ratios is positive? In quadrant 2 what is the ratios is positive? In quadrant 3 what is the ratios is positive? In quadrant 4 what is the ratios is positive?
500
sin7π/8=sin π/8 tan 5π/4=tan π/4 cos 11π/6= cosπ/6
What is sin7π/8=? tan 5π/4=? cos 11π/6=?
500
sin(x-π)=-sinx cos(x+3π/2)=sinx tan(2π-x)=-tanx
What is sin(x-π)=? cos(x+3π/2)=? tan(2π-x)=?
500
=sin^2x+cos^2x+tan^2x =(sin^2x+cos^2x)+tan^2x =1+tan^2x =cos^2x/cos^2x + sin^2x/cos^2x =1/cos^2x =sec^2x
What is sec^2x=sin^2x+cos^2x+tan^2x how to proof?
500
vertical strecth by a factor of 5 Horizontal compression by a factor of 1/4 Horizontal translation right by 3 units Vertical translation up by 9 units
Describe the y=5sin(4(x-3))+9 translation and find it period.
500
csc5π/6=2 Sec5π/6=2
What is csc 5π/6=? Sec 5π/6=?