Trigonometic Identities

Question 1

Csc(theta)=

Answer 1

1/sin(theta)

Question 2

Sec(theta)=

Answer 2

1/cos(theta)

Question 3

Tan(theta)=

Answer 3

Sin(theta)/cos(theta)

Question 4

Cot(theta)=

Answer 4

1/tan(theta) = Cos(theta)/sin(theta)

Question 5

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

Answer 5

1

Question 6

Tan^2(theta) +1=

Answer 6

sec^2(theta)

Question 7

1 - cot^2(theta)=

Answer 7

Csc^2(theta)

Question 8

Sin(- theta)=

Cos(- theta)=

Answer 8

-sin(theta)

Cos(theta)

Question 9

Sin(theta + 2(Pi))=

Cos(theta + 2(Pi))=

Answer 9

Sin(theta)
Cos(theta)
(2(Pi) = 360 degrees i.e. full rotation

Question 10

Sin(x + y)=
Sin(x - y)=

Cos(x + y)=
Cos(x - y)=

Answer 10

Sin(x)Cos(y) + Cos(x)Sin(y)
Sin(x)Cos(y) - Cos(x)Sin(y)

Cos(x)Cos(y) - Sin(x)Sin(y)
Cos(x)Cos(y) + Sin(x)Sin(y)

Question 11

Tan(x + y)=

Tan(x - y)=

Answer 11

[Tan(x) +Tan(y)]/[1 - Tan(x)Tan(y)]

[(Tan(x) - Tan(y)]/[(1 + Tan(x)Tan(y)]

Question 12

Sin(2x)=

Cos(2x)=

Answer 12

2sin(x)cos(x)

cos^2(x)sin^2(x)
Or
2cos^2(x) - 1
Or
1 - 2sin^2(x)

Question 13

Cos^2(x)=

Sin^2(x)=

Answer 13

[1 + cos(2x)]/2

[1 - cos(2x)]/2

Question 14

Sin(x)cos(y)=
Cos(x)cos(y)=
Sin(x)sin(y)=

Answer 14

1/2[sin(x+y) + sin(x-y)]
1/2[cos(x+y) + cos(x-y)]
1/2[cos(x-y) - cos(x+y)]