Trigonometric, exponential and logarithmic functions

Question 1

What is an even function

Answer 1

If f(-x)=f(x)

Question 2

what is an odd function

Answer 2

if f(-x)=-f(x)

Question 3

decomposition into an even function

Answer 3

f(x)=1/2(f(x)+f(-x))

Question 4

decomposition into an odd function

Answer 4

f(x)=1/2(f(x)-f(-x))

Question 5

inverse function of y=f(x)

Answer 5

x=f^-1(y)

Question 6

sin(0)

Answer 6

0

Question 7

sin(pi)

Answer 7

0

Question 8

sin(3pi/2)

Answer 8

-1

Question 9

sin(2pi)

Answer 9

0

Question 10

cos(0)

Answer 10

1

Question 11

cos(pi/2)

Answer 11

-1

Question 12

cos(3pi/2)

Answer 12

0

Question 13

cos(2pi)

Answer 13

1

Question 14

sin(pi/4)

Answer 14

1/rt2

Question 15

sin(pi/3)

Answer 15

rt3/2

Question 16

sin(pi/6)

Answer 16

1/2

Question 17

cos(pi/4)

Answer 17

1/rt2

Question 18

cos(pi/3)

Answer 18

1/2

Question 19

cos(pi/6)

Answer 19

rt3/2

Question 20

sin(-𝜃 )

Answer 20

-sin(𝜃 )

Question 21

sin(pi/2-𝜃 )

Answer 21

cos(𝜃 )

Question 22

sin(𝜃 +pi)

Answer 22

-sin(𝜃 )

Question 23

cos(-𝜃 )

Answer 23

cos(𝜃 )

Question 24

cos(pi/2-𝜃 )

Answer 24

sin(𝜃 )

Question 25

cos(𝜃 +pi)

Answer 25

-cos(𝜃 )

Question 26

sec(x)

Answer 26

1/cos(x)

Question 27

csc(x)

Answer 27

1/sin(x)

Question 28

cot(x)

Answer 28

1/tan(x)

Question 29

exp(t+s)

Answer 29

exp(t)exp(s)

Question 30

inverse of x=logb(y)

Answer 30

y=b^x

Question 31

b^logbx

Answer 31

logb(b^x)

Question 32

inverse of y=e^x

Answer 32

x=ln(y)

Question 33

e^ln(x)

Answer 33

ln(e^x)

Question 34

e^0

Answer 34

1

Question 35

e^1

Answer 35

e

Question 36

ln(1)

Answer 36

0

Question 37

ln(e)

Answer 37

1

Question 38

e^t*e^s

Answer 38

e^t+s

Question 39

ln(ab)

Answer 39

ln(a)+ln(b)

Question 40

e^t/e^s

Answer 40

e^t-s

Question 41

ln(a/b)

Answer 41

ln(a)-ln(b)

Question 42

e^t^a

Answer 42

e^at

Question 43

ln(a^b)

Answer 43

bln(a)

Question 44

change of base - ln(y)

Answer 44

ln(b)logb(y)

Question 45

polar representation of x

Answer 45

rcos(𝜃)

Question 46

polar representation of y

Answer 46

rsin(𝜃)

Question 47

Euler’s formula

Answer 47

z=r(cos(𝜃)+isin(𝜃))=re^i𝜃

Question 48

cos(𝜃) - complex exponential

Answer 48

(e^i(𝜃)+e^-i(𝜃))/2

Question 49

sin(𝜃) - complex exponential

Answer 49

(e^i(𝜃)-e^-i(𝜃))/2i

Question 50

cosh(x)

Answer 50

(e^x+e^-x)/2

Question 51

sinh(x)

Answer 51

(e^x-e^-x)/2

Question 52

tanh(x)

Answer 52

(e^x-e^-x)/(e^x+e^-x)

Question 53

sech(x)

Answer 53

1/cosh(x)

Question 54

csch(x)

Answer 54

1/sinh(x)

Question 55

coth(x)

Answer 55

1/tanh(x)

Question 56

sin(a+b)

Answer 56

sin(a)cos(b)+cos(a)sin(b)

Question 57

cos(a+b)

Answer 57

cos(a)cos(b)-sin(a)sin(b)

Question 58

sin(a-b)

Answer 58

sin(a)cos(b)-cos(a)sin(b)

Question 59

cos(a-b)

Answer 59

cos(a)cos(b)+sin(a)sin(b)

Question 60

De Moivre’s - cos(n𝜃)+isin(n𝜃)

Answer 60

e^in𝜃=(e^i𝜃)^n=(cos(𝜃)+isin(𝜃))^n

Question 61

cosh^2(x)-sinh^2(x)

Answer 61

1