Checkpoint

Question 1

Sin^2(x) + cos^2(x) =?

Answer 1

1

Question 2

1 + tan^2(x) =?

Answer 2

sec^2(x)

Question 3

Sin(2x) =?

Answer 3

2sin(x)cos(x)

Question 4

1 + cot^2(x) =?

Answer 4

csc^2(x)

Question 5

Cos(2x) =?

Answer 5

2cos^2(x) - 1

Question 6

SinACosB =?

Answer 6

[sin(A - B) + sin(A + B)] / 2

Question 7

SinAsinB =?

Answer 7

[cos(a-b) - cos(A + B)] / 2

Question 8

CosACosB = ?

Answer 8

[cos(A - B) + cos (A + B)]/2

Question 9

Derivative of sinx?

Answer 9

cosx

Question 10

Derivative of cosx?

Answer 10

-sinx

Question 11

Derivative of tanx?

Answer 11

sec^2(x)

Question 12

Derivative of secx?

Answer 12

secxtanx

Question 13

derivitive of cscx?

Answer 13

-Cscxcotx

Question 14

Antiderivitive of cosx?

Answer 14

Sin(x) + C

Question 15

derivitive of cotx?

Answer 15

-csc^2(x)

Question 16

Antiderivitive of sinx?

Answer 16

-Cosx + C

Question 17

Antiderivitive of tanx?

Answer 17

Ln|secx| + c

Question 18

Antiderivitive of secx?

Answer 18

Ln|secx + tanx| + c

Question 19

Antiderivitive of cscx?

Answer 19

-Ln|cscx + cotx| + C

Question 20

Antiderivitive of cot?

Answer 20

Ln|sinx| + c

Question 21

Antiderivitive of sec^2(x)

Answer 21

Tanx + C

Question 22

Antiderivitive of csc^2(x)

Answer 22

-cotx

Question 23

Antiderivitive of secxtanx

Answer 23

secx

Question 24

Antiderivitive of cscxcotx

Answer 24

-Csc(x)

Question 25

Sin^m times cos^n

Answer 25

If n odd: substitute u = sinx, du = cosx. Leave an even power of cosine
If m odd: substitute u = cosx, du = -sinx. Leave an even power of sine.
If both even revert to odd

Question 26

Tan^m times sec^n

Answer 26

If n even: substitute u = tanx and du = sec^2(x). Use trig identity 1 + tan^2 = sec^2(x)

if m odd: substitute u = secx and du = secxtanx. Use the trig identities to convert the remaining factors in terms of secxtan^2(x) = sec^2(x) - 1 = u^2 - 1

Question 27

a^2 + x^2 =

Answer 27

X = atan0

Question 27

a^2 - x^2 =

Answer 27

X = asin0

Question 27

x^2 - a^2 =

Answer 27

X = asec0