values of trigonometric functions of particular angles

 taking the angle in degree measure

 

 sin(0)=0

cos(0)=1

tan(0)=0

 

sin(90)=1

cos(90)=0

tan(90)=infinity

 

sin(30)=1/2

cos(30)=[( sqrt(3) ) / 2]

tan(30)=1 / {sqrt(3)}

 

 

sin(60)=[( sqrt(3) ) / 2]

cos(60)=1/2

tan(60)= {sqrt(3)}

 

sin(45) ={ 1 / [  sqrt(2) ] }

cos(45) ={ 1 / [  sqrt(2) ] }

tan(45)=1

 

  trigonometry identities

 

1.Prove that 2cos(pi/13)cos(9pi/13)+cos (3pi/13)+cos(5pi/13) = 0
solution 

2. Prove that ( sin3x + sinx ) sinx + (cos3x - cosx) cosx = 0

solution

3. Prove that (cosx +cosy)^2 + ( sinx - siny )^2 = 4 { cos[(x+y)/2] }^2

solution

4. Prove that (cosx - cosy)^2 + ( sinx - siny )^2 = 4 { sin[(x-y)/2] }^2

solution 




5.Show that sinx +sin3x+ sin5x +sin7x = 4cosx cos2x sin 4x

solution

6. Show that [sin7x+sin5x +sin9x+sin3x] / [cos7x+cos5x+cos9x+cos3x] = tan6x

solution


7. Prove that sin3x+sin2x-sinx = 4sin(x)cos(x/2)cos(3x/2)
solution




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