Trig Identities

Question 1

Derivative of Sinx

Answer 1

Cosx

Question 2

Derivative of cosx

Answer 2

-sinx

Question 3

Derivative of tanx

Answer 3

Sec^2x

Question 4

Derivative of cotx

Answer 4

-csc^2x

Question 5

Derivative of secx

Answer 5

Secxtanx

Question 6

Derivative of cscx

Answer 6

-cscx cotx

Question 7

Derivative of ln(|sec|)

Answer 7

tanx

Question 8

1- sin^2 = ?

Answer 8

Cos^2

Question 9

Tan^2 + 1 = ?

Answer 9

Sec^2

Question 10

Cot^2 + 1 = ?

Answer 10

Csc^2

Question 11

a^2 - x^2

Answer 11

X = asin(theta)

Question 12

a^2 + x^2

Answer 12

X= atan(theta)

Question 13

x^2 - a^2

Answer 13

x = asec(theta)

Question 14

Sin(u)sin(v)

Answer 14

(1/2)(cos(u-v) - cos(u+v))

Question 15

Cos(u)cos(v)

Answer 15

(1/2)(cos(u-v) + cos(u+v))

Question 16

Sin(u)cos(v)

Answer 16

(1/2)(sin(u+v) + sin(u-v))

Question 17

Cos(u)sin(v)

Answer 17

(1/2)(sin(u+v) - sin(u-v))

Question 18

Law of cooling (y ’ form)

Answer 18

y ‘ = -k(y - t°)

Question 19

Law of cooling (general form)

Answer 19

y= t° + Ce^(-kt)

Question 20

Continuous Annuity (general form)

Answer 20

P(t) = (N/r) + Ce^(rt)

Question 21

Logistics equation

Answer 21

P ‘(t) = kP(t)(M-P(t))

Question 22

Population model

Answer 22

P = (CMe^(kMt)) / (1+ Ce^(kMt))

Question 23

Sin(2 theta)

Answer 23

2sin(x) cos(x)

Question 24

Cos(2x)

Answer 24

Cos^2x - sin^2x