# Trigonometry (Right Triangle)

See how to find the trigonometric ratios in a right triangle

(sine, cosine, tangent, cosecant, secant, cotangent).

12 examples and their solutions.

## Sine

### Formula

sin θ = (opposite side)(hypotenuse)

### Example

sin θ = ?

Solution sin θ = 35

Close

### Example

sin θ = ?

Solution sin θ = 1213

Close

### Example

sin θ = 45, x = ?

Solution sin θ = x10 = 45

x = 45⋅10

= 4⋅2

= 8

Close

## Cosine

### Formula

cos θ = (adjacent side)(hypotenuse)

### Example

cos θ = ?

Solution cos θ = 45

Close

### Example

cos θ = ?

Solution cos θ = 513

Close

### Example

## Tangent

### Formula

tan θ = (opposite side)(adjacent side)

### Meaning

### Example

tan θ = ?

Solution tan θ = 34

Close

### Example

tan θ = ?

Solution tan θ = 125

Close

### Example

tan θ = 76, x = ?

Solution tan θ = x12 = 76

x = 76⋅12

= 7⋅2

= 14

Close

## Cosecant

### Formula

csc θ = 1sin θ

= 1(opposite side)(hypotenuse)

### Example

csc θ = ?

Solution x

^{2}+ 3

^{2}= 4

^{2}- [1]

x

^{2}+ 9 = 16

x

^{2}= 7

x = √7 - [2] [3]

[3]

x > 0

↓

csc θ = 1sin θ

= 1√74

= 4√7⋅√7√7 - [4]

= 4√77

Close

## Secant

### Formula

sec θ = 1cos θ

= 1(adjacent side)(hypotenuse)

### Example

sec θ = ?

Solution x

^{2}= 1

^{2}+ 2

^{2}- [1]

= 1 + 4

= 5

x = √5 - [2] [3]

[3]

x > 0

↓

sec θ = 1cos θ

= 11√5

= √51 - [4]

= √5

Close

## Cotangent

### Formula

cot θ = 1tan θ

= 1(opposite side)(adjacent side)

### Example

cot θ = ?

Solution x

^{2}+ 2

^{2}= 5

^{2}- [1]

x

^{2}+ 4 = 25

x

^{2}= 21

x = √21 - [2] [3]

[3]

x > 0

↓

cot θ = 1tan θ

= 12√21

= √212 - [4]

Close