Question

trigonometric formulas

Answer 1

basics:  sinФ=opp side/hypotenuse
             cosФ=adj side/hyp
             tanФ=opp side/adj side
             cotФ=adj side/op side
             cosecФ=1/sinФ
             secФ=1/cosФ

intermediate:
  sin(a+b)= sina.cosb+cosa.sinb
  cos(a+b)=cosacosb-sinasinb
  sin²Ф+cos²Ф=1
 1+tan²Ф=sec²Ф
1+cot²Ф=cosec²Ф
enough for a homework

  Ф is the angle
  

Answer 2

for angle A
sin^2A+cos^2A=1
sec^2A-tan^2a=1
cossec^2A-cot^2A=1
sinA=1/cossecA
cosA=1/secA
tanA=1/cotA
sinA=cos(90-A)
tanA=cot(90-A)
cossecA=sec(90-A)
sin2A=2sinA*cosA
cos2A=cos^2A-sin^2A
          =1-2sin^2A
           =2cos^2A-1
sin(A+B)=sinA*cosB+cosAsinB
sin(A-B)=sinAcosB-cosAsinB
cos(A+B)=cosA*cosB-sinA*sinB
cos(A-B)=cosAcosB+sinAsinB
tan(A+B)=(tanA+tanB)/1-tanAtanB
tan(A-B)=(tanA-tanB)/1+tanAtanB
2sinAcosB=sin(A+B)+sin(A-B)
2cosAsinB=sin(A+B)-sin(A-B)
2cosAcosB=cos(A+B)+cos(A-B)
2sinAsinB=cos(A-B)-COS(A+B)
sin(A+B)sin(A-B)=sin^2A-sin^2B
cos(A+B)cos(A-B)=cos^2A-sin^2B