Trigonomic Functions

Question 1

Recipricol

Cot(x)

Answer 1

1/tan(x)

Question 2

Reciprocal

Sec(x)=

Answer 2

1/cos(x)

Question 3

Reciprocal

Csc(x)=

Answer 3

1/sin(x)

Question 4

Quotient

Tan(x)=

Answer 4

Sin(x)/Cos(x) = sec(x)/csc(x)

Question 5

Quotient

Cot(x) =

Answer 5

Cos(x)/Sin(x) = Csc(x)/Sec(x)

Question 6

Pythagorean

Cos^2(x) + Sin^2(x) =

Answer 6

1

Question 7

Pythagorean

1+ tan^2(x) =

Answer 7

Sec^2(x)

Question 8

Pythagorean

Cot^2(x) + 1=

Answer 8

Csc^2(x)

Question 9

Odd-even

Sin(-x) =

Answer 9

-sin(x)

Question 10

Odd-even

Cos(-x) =

Answer 10

Cos(x)

Question 11

Odd-even

Tan(-x) =

Answer 11

-Tan(x)

Question 12

Composite-Argument

Cos(a-b) =

Answer 12

Cos(a)Cos(b) + sin(a)sin(b)

Question 13

Composite argument

cos(a+b) =

Answer 13

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

Question 14

Composite argument

Sin(a-b) =

Answer 14

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

Question 15

Composite argument

Sin(a+b) =

Answer 15

Sin(a)Cos(b) + Cos(a)Sin(b)

Question 16

Composite arguments

Tan(a-b) =

Answer 16

(tan(a)-tan(b)) / (1+tan(a)tan(b))

Question 17

Composite arguments

tan(a+b) =

Answer 17

(tan(a)+tan(b)) / (1-tan(a)tan(b))

Question 18

Double argument

Sin(2x) =

Answer 18

2sin(x)cos(x)

Question 19

Doluble argument

Cos(2x) =

Answer 19

=Cos^2(x)-sin^2(x)

=1-2sin^(x)

=2cos^2(x) - 1

Question 20

Double argument

Tan(2x) =

Answer 20

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

Question 21

half argument

Sin(1/2x) =

Answer 21

土𠂆(0.5(1-cos(x)))

Question 22

Half argument

Cos(1/2x) =

Answer 22

土𠂆(0.5(1+cos(x)))

Question 23

Half argument

Tan(1/2) =

Answer 23

= 土𠂆( (1-cos(x)) / (1+cos(x)) )

= sin(x) / (1+cos(x))

= (1-cos(x)) / sin(x)