Trigonometric Identities

Terms

undefined, object
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cotangent ϴ

(abbreviation)
cot ϴ
secant ϴ

(abbreviation)
sec ϴ
cosecant ϴ

(abbreviation)
csc ϴ
cot ϴ

(full name)
cotangent ϴ
sin ϴ

(reciprocal)
1
â”€â”€â”€â”€
csc Ï´
cos ϴ

(reciprocal)
1
â”€â”€â”€â”€
sec Ï´
sec ϴ

(full name)
secant ϴ
tan ϴ

(reciprocal)
1
â”€â”€â”€â”€
cot Ï´
csc ϴ

(reciprocal)
1
â”€â”€â”€â”€
sin Ï´
sec ϴ

(reciprocal)
1
â”€â”€â”€â”€
cos Ï´
csc ϴ

(full name)
cosecant ϴ
cot ϴ

(reciprocal)
1
â”€â”€â”€â”€
tan Ï´
tan ϴ

(ratio)
sin Ï´
â”€â”€â”€â”€
cos Ï´
sin ϴ

(definition)
y
â”€
r
cot ϴ

(ratio)
cos Ï´
â”€â”€â”€â”€
sin Ï´
cos ϴ

(definition)
x
â”€
r
tan ϴ

(definition)
y
â”€
x
cot ϴ

(definition)
x
â”€
y
sec ϴ

(definition)
r
â”€
x
csc ϴ

(definition)
r
â”€
y
Pythagorean Identity?
cos²ϴ + sin²ϴ = 1
What is:

cos²ϴ + sin²ϴ = 1
The Pythagorean Identity.
Simplify:

(cos²ϴ + sin²ϴ)/cos²ϴ = 1/cos²ϴ
1 + tan²ϴ = sec²ϴ
Simplify:

(cos²ϴ + sin²ϴ)/sin²ϴ = 1/sin²ϴ
cot²ϴ + 1 = csc²ϴ
Express in terms of sin & cos:

1 + tan²ϴ = sec²ϴ
(cos²ϴ + sin²ϴ)/cos²ϴ = 1/cos²ϴ
Express in terms of sin & cos:

cot²ϴ + 1 = csc²ϴ
(cos²ϴ + sin²ϴ)/sin²ϴ = 1/sin²ϴ

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