Identities for Trigs

Question 1

sec(x)

Answer 1

1/cos(x)

Question 2

Sine double angle identity: Sin(2x)

Answer 2

2sin(x)cos(x)

Question 3

Adjacent / Hypotenuse is

Answer 3

cos(θ)

Question 4

Opposite / Adjacent

Answer 4

tan(θ)

Question 5

x = arcsec(theta)

Answer 5

sqrt(x^2-a^2)

Question 6

sin(θ) =

Answer 6

Opposite / Hypotenuse

Question 7

tan(x) =

Answer 7

sin(x)/cos(x)

Question 8

cos(x)/1

Answer 8

1/sec(x)

Question 9

derive: ln(sec(x)+tan(x)) + C

Answer 9

sec(x)

Question 10

integral: sin(2x)

Answer 10

-1/2cos(2x)+c

Question 11

csc(x)

Answer 11

1/sin(x)

Question 12

Opposite / Hypotenuse is

Answer 12

sin(θ)

Question 13

Hypotenuse / Opposite is

Answer 13

csc(θ)

Question 14

Tan^2(x) =

Answer 14

Sec^2(x)-1

Question 15

sec(θ) =

Answer 15

Hypotenuse / Adjacent

Question 16

integrade: 5^x

Answer 16

(5^x)/ln(5) + c

Question 17

Reduce sin(x)cos(x) =

Answer 17

1/2sin(2x)

Question 18

Trapezoidal Rule

Answer 18

Tn = (b-a/2n)*[f(Xo)+2f(x1)+2f(x2)…+2f(xn-1)+f(xn)] ***no coefficient 2 in the first and last terms.

Question 19

1/cot(x)

Answer 19

tan(x)/1

Question 20

Simpson’s Rule

Answer 20

Sn = (b-a/3n)*[f(Xo)+4f(x1)+2f(x2)+4f(x3)+2f(x4)….2f(xn-2)+4f(xn-1)+f(xn)] … n must be EVEN integer.

Question 21

x = arcsin(theta)

Answer 21

sqrt(a^2-x^2)

Question 22

integral: cos(2x)

Answer 22

1/2sin(2x)+c

Question 23

1/cos(x)

Answer 23

sec(x)

Question 24

x = arctan(theta)

Answer 24

sqrt(a^2+x^2)

Question 25

1/sin(x)

Answer 25

csc(x)

Question 26

csc(θ) =

Answer 26

Hypotenuse / Opposite

Question 27

Sin^2(x) =

Answer 27

1-Cos^2(x)

Question 28

1/n-1(sec^n-2(x))(tan(x)+(n-2/n-1) integral sec^n-2(x) DX

Answer 28

integrade sec^n(x)DX

Question 29

Hypotenuse / Adjacent is

Answer 29

sec(θ)

Question 30

cot(x)

Answer 30

1/tan(x)

Question 31

Cos^2(x) =

Answer 31

1-Sin^2(x)

Question 32

Derive: tan(x)

Answer 32

sec^2(x)

Question 33

sin(x)/1

Answer 33

1/csc(x)

Question 34

Reduce Cos^2(x)

Answer 34

1/2(1+cos(2x))

Question 35

1+Tan^2(x) =

Answer 35

Sec^2(x)

Question 36

sqrt(a^2+x^2)

Answer 36

x = arctan(theta)

Question 37

Sn = (b-a/3n)*[f(Xo)+4f(x1)+2f(x2)+4f(x3)+2f(x4)….2f(xn-2)+4f(xn-1)+f(xn)] … n must be EVEN integer.

Answer 37

Simpson’s Rule

Question 38

1/sec(x)

Answer 38

cos(x)/1

Question 39

sqrt(x^2-a^2)

Answer 39

x = arcsec(theta)

Question 40

tan(θ) =

Answer 40

Opposite / Adjacent

Question 41

sqrt(a^2-x^2)

Answer 41

x = arcsin(theta)

Question 42

1/tan(x)

Answer 42

cot(x)

Question 43

cot(θ) =

Answer 43

Adjacent / Opposite

Question 44

Reduce Sin^2(x)

Answer 44

1/2(1-cos(2x))

Question 45

2sin(x)cos(x)

Answer 45

Sine double angle identity: Sin(2x)

Question 46

tan(x)/1

Answer 46

1/cot(x)

Question 47

Derive: (5^x)/ln(5)

Answer 47

5^x

Question 48

sin(x)/cos(x)

Answer 48

tan(x)

Question 49

integrade: sec^n(x)DX

Answer 49

1/n-1(sec^n-2(x))(tan(x)+(n-2/n-1) integral sec^n-2(x) DX

Question 50

E = (b-a)^3/12n^2 * M (f’‘(x))

Answer 50

Trapezoidal Error Rule

Question 51

Tn = (b-a/2n)*[f(Xo)+2f(x1)+2f(x2)…+2f(xn-1)+f(xn)] ***no coefficient 2 in the first and last terms.

Answer 51

Trapezoidal Rule

Question 52

cos(θ) =

Answer 52

Adjacent / Hypotenuse

Question 53

1/csc(x)

Answer 53

sin(x)/1

Question 54

Integral Tan(x)

Answer 54

ln(secx) or -ln(cosx)

Question 55

integrade: sec(x) DX

Answer 55

ln(sec(x)+tan(x)) + C

Question 56

integrade: sec^2(x) DX

Answer 56

tan(x) + c

Question 57

Trapezoidal Error Rule

Answer 57

E = (b-a)^3/12n^2 * M (f’‘(x))

Question 58

Adjacent / Opposite is

Answer 58

cot(θ)

Question 59

Simpson’s Error Rule

Answer 59

E = (b-a)^5/180n^4 * M(f’’’‘(x))[4th derivative]

Question 60

E = (b-a)^5/180n^4 * M(f’’’‘(x))[4th derivative]

Answer 60

Simpson’s Error Rule

Question 61

1/2sin(2x)

Answer 61

Reduce sin(x)cos(x) =