Trig

Question 1

What is the reciprocal identity for sin(x)?

Answer 1

1 / csc(x)

Question 2

What is the reciprocal identity for cos(x)?

Answer 2

1 / sec(x)

Question 3

What is the reciprocal identity for tan(x)?

Answer 3

1 / cot(x)

Question 4

What is the reciprocal identity for csc(x)?

Answer 4

1 / sin(x)

Question 5

What is the reciprocal identity for sec(x)?

Answer 5

1 / cos(x)

Question 6

What is the reciprocal identity for cot(x)?

Answer 6

1 / tan(x)

Question 7

What are the 3 Pythagorean identities?

Answer 7

1. sin^2(x) + cos^2(x) = 1
2. tan^2(x) + 1 = sec^2(x)
3. cot^2(x) + 1 = csc^2(x)

Question 8

What is the double angle identity for sin2(x)?

Answer 8

2sin(x) * cos(x)

Question 9

What are the double identities for cos2(x)?

Answer 9

1. cos^2(x) - sin^2(x)
2. 1 - 2 sin^2(x)
3. 2cos^2(x) - 1

Question 10

What is the double angle identity for tan2(x)?

Answer 10

2tan(x) / 1 - tan^2(x)

Question 11

What are the derivatives of y = sin x?

Answer 11

y’ = cos x

Question 12

What are the derivatives of y = cos x?

Answer 12

y’ = - sin x

Question 13

What are the derivatives of y = tan x?

Answer 13

y’ = sec^2 x

Question 14

What are the derivatives of y = cot x?

Answer 14

y’ = -csc^2 x

Question 15

What are the derivatives of y = sec x?

Answer 15

y’ = sec x tan x

Question 16

What are the derivatives of y = csc x?

Answer 16

y’ = -csc x cot x

Question 17

What is the derivative of the exponential function?

Answer 17

f’(x) = b^x ln(b)

Question 18

What is the derivative of the logarithmic function?

Answer 18

f’(x) = 1 / x ln (b)

Question 19

What is the derivative for the inverse sin function?

Answer 19

f’(x) = 1/√1-x²

Question 20

What is the derivative of the inverse cos function?

Answer 20

f’(x) = -1/√1-x²

Question 21

What is the derivative of the inverse tan function?

Answer 21

f’(x) = 1/(1+x²)

Question 22

What is the derivative of the inverse csc function?

Answer 22

f’(x) = -1/(|x|√x²-1)

Question 23

What is the derivative of the inverse sec function?

Answer 23

1/(|x|√x²-1)

Question 24

What is the derivative of the inverse cot function?

Answer 24

-1/(1+x²)