Core 3 Trigonometry

Core 3 Trigonometry

1. The 3 basic trig functions

   • y = sin(x)
     • The reciprocal is cosec(x)
       • cosec(x) = 1 / sin(x)
   • y = cos(x)
     • The reciprocal is sec(x)
       • sec(x) = 1/ cos(x)
   • y = tan(x)
     • The reciprocal is cot (x)
       • cot(x) = 1 / tan(x)

2. Special Triangles

3. Trig identities

   • Tan(x) = sin(x) / cos(x)
     • Cot(x) = cos(x) / sin(x)
   • sin^2 (x) + cos^2 (x) = 1
     • Divide by cos^2(x)
       • tan^2(x) + 1 = sec^2(x)
     • Divide by sin^2(x)
       • 1 + cot^2(x) = cosec^2(x)
   • tan(x) = cot(90 - x)

4. Quadrants

   • Use Quadrants to work out the sign and magnitude of an angle's trigonomentric ratio
   • Letters denote which function is positive

5. Check whether the answer needs to be in radians or degrees

6. Inverse trig functions

   • i.e. sin(x)=5 To find x you would use the inverse arcsin(5) =x
   • Arcsin(x) Arccos(x) Arctan(x
   • Reflect the graph of the original in y=x

7. Addition formula

   • sin (A + B) = sin(A)cos(B) + cos(A)sin(B)
   • cos(A+B) = cos(A)cos(B) - sin(A)sin(B)
     • The signs switch
   • tan(A+B) = ( tan(A)+tan(B) ) / 1 - tan(A)tan(B)
     • The sign switch on the denominator

8. Double angle formulae

   • Divide by factor of A for other multiples
     • i.e. to find sin(3A)
   • sin(2A) = 2sin(A)cos(A)
   • Cos(2A) = cos^2(A) - sin^2(A)
     • cos^2(A) -1
     • 1- 2sin^2(A)
   • tan(2A) = 2tan(A) / 1 - tan^2(A)

9. Half-angle formulae

   • for (A/2)
   • cos^2(A/2) = 1/2 ( 1+ cos(A) )
   • sin^2(A/2) = 1/2 ( 1 - cos(A) )

10. Acos(x) + B sin(x)

    • Can be expressed in forms Rcos (x + alpha) or Rsin (x + alpha
    • R = √(A^2+B^2 )
    • tan alpha = b/a or tan alpha = a/b

11. Square root + and - Write out all working

Images and files in the map