Trig identities Flashcards
tan (x) =
sin(x) / cos(x)
cot(x)=
cos(x) / sin(x)
or
1/tan(x)
sec(x)=
1/cos(x)
csc(x)=
1/sin(x)
What is the Pythagorean identity?
sin^2(x) + cos^2(x)= 1
cos^2(x)=
1-sin^2(x)
sin^2(x)=
1-cos^2(x)
csc^2(x)=
1+cot^2(x)
sec^2(x)=
1+tan^2(x)
sin(2x)
2sin(x)cos(x)
cos(2x)
cos^2(x) - sin^2(x)
or
2cos^2(x)-1
or
1-2sin^2(x)
tan(2x)=
2tan(x) / (1-tan^2(x))
sin (x/2)=
√(1-cos(x)) / 2
cos (x/2) =
√(1+cos(x)) / 2
tan (x/2) =
(1-cos(x)) / sin(x)
sin(x) / (1+cos(x))
√(1-cos(x) / 1+ cos(x)
cos (A + B)
cos(A)cos(B)-sin(A)sin(B)
sin (A+B)
sin (A)cos(B) - cos(A)sin(B)
sin^2(x) (double angle)
1/2 (1-cos(2A))
cos^2(A) (half angle) =
1/2 (1+cos(2A)
Sin(A)sin(B) =
1/2 (cos(A-B) - cos(A+B))
cos(A)cos(B)=
1/2 (cos(A-B)+cos(A+B))
sinAcosB
1/2 (sin(A-B) + sin (A+B)
sin’(x)
cos(x)
cos’(x)
-sin (x)
tan’ (X)
sec^2(x)
sec’(x)
sec(x)tan(x)
csc’(x)
-csc(x)cot(x)
cot’(x)
-csc^2(x)
∫sin(x) dx
-cos(x) + C
∫ cos(x)dx
sin (x) +C
∫ tan(x) dx=
ln|sec(x)| + C
∫csc(x) dx
ln |csc(x) -cot(x)| +C
∫sec(x) dx
ln |secx) + tan(x)| +C
∫cot(x) dx
-ln |csc(x)| + C
what is the range of arc cos, arc cot, arc sec ?
(0,π)
what is the rang of arcsin, arctan, arc csc?
(π/2, -π/2)
