Trigonometric Functions

Question 1

Secant = sec x

Answer 1

1
———
cos x

Question 2

Cosecant = cosec x

Answer 2

1
———
sin x

Question 3

Cotangent = cot x

Answer 3

1 cos x
——— = ———
tan x sin x

Question 4

sec^2 x

Answer 4

1 + tan^2 x

Question 5

cosec^2 x

Answer 5

1 + cot^2 x

Question 6

sin(A+B)

Answer 6

sinAcosB + cosAsinB

Question 7

sin(A-B)

Answer 7

sinAcosB - cosAsinB

Question 8

cos(A+B)

Answer 8

cosAcosB - sinAsinB

Question 9

cos(A-B)

Answer 9

cosAcosB + sinAsinB

Question 10

tan(A+B)

Answer 10

tanA + tanB
——————
1 - tanAtanB

Question 11

tan(A-B)

Answer 11

tanA - tanB
——————
1 + tanAtanB

Question 12

Differentiate y = sin kx

Answer 12

dy .
— = k cos kx
dx .

Question 13

Differentiate y = cos kx

Answer 13

dy .
— = - k sin kx
dx .

Question 14

Differentiate y = tan kx

Answer 14

dy
— = k sec^2 kx
dx

Question 15

Differentiate y = e^kx

Answer 15

dy .
— = k e^kx
dx .

Question 16

Differentiate y = ln (kx^n)

Answer 16

dy 1 d(kx^n)
— = ——— x ————
dx kx^n dx

Question 17

Differentiate y = ln (kx)

Answer 17

dy d 1
— = —— (ln k + ln x) = —
dx dx x

Question 18

Differentiate y = a^kx

Answer 18

dy d(kx)
— = —— x a^kx ln(a)
dx dx

Question 19

Chain Rule y (f(x))

Answer 19

dy dy du
— = — x — Outside times inside
dx du dx

Question 20

Product Rule y = uv

Answer 20

dy dv du
— = u — + v —
dx dx dx

Question 21

. u
Quotient Rule y = —
v

Answer 21

.                   du           dv
                  v —    -   u —
dy                dx           dx
—  =   ——————————
dx                         v^2

Question 22

differentiate y = cosec kx

Answer 22

dy d(kx)
— = —— x - cosec (kx) cot (kx)
dx dx

Question 23

Differentiate y = sec kx

Answer 23

dy d(kx)
— = —— x sec (kx) tan (kx)
dx dx

Question 24

Differentiate y = cot kx

Answer 24

dy d(kx)
— = —— x - cosec^2 (kx)
dx dx

Question 25

Differentiate y = arcsin x

Answer 25

dy 1
— = ——————
dx (1- x^2)^1/2

Question 26

Differentiate y = arccos x

Answer 26

dy - 1
— = ——————
dx (1- x^2)^1/2

Question 27

Differentiate y = arctan x

Answer 27

dy 1
— = ————
dx 1+ x^2

Question 28

cos^2 x

Answer 28

1+cos2x
————
2

Question 29

sin^2 x

Answer 29

1 - cos2x
————
2

Question 30

Differentiate u(x)^n
u = trig angle

Answer 30

n * u(x)^(n-1) * u’(x)