# How do I find cos 180

### Many angles - one sine value

The sine of 30 ° is 0.5. If you continue walking around the unit circle, you will see that the sine of 150 ° is also equal to 0.5.

$$ sin (30 ^ °) = sin (150 ^ °) = 0.5 $$

How exactly is the relationship between different angles and the same sine values?

The right triangle is mirrored on the y-axis.

The 150 ° angle results from $$ 180 ^ ° -30 ^ ° $$ or generally $$ 180 ^ ° -alpha $$.

Degree | Radians |

$$ sin (alpha) = sin (180 ^ ° -alpha) $$ | $$ sin (x) = sin (pi-x) $$ |

In memory of:

$$ pi $$ in radians corresponds to 180 ° in degrees.

### More relationships

If you continue to wander on the unit circle, even more relationships arise.

**Example:**

$$ sin (30 ^ °) = 0.5 $$ and $$ sin (210 ^ °) = - 0.5 $$.

In general:

Degree | Radians |

$$ sin (alpha) = - sin (180 ^ ° + alpha) $$ | $$ sin (x) = - sin (pi + x) $$ |

And this relationship here:

**Example:**

$$ sin (30 ^ °) = 0.5 $$ and $$ sin (330 ^ °) = - 0.5 $$.

Degree | Radians |

$$ sin (alpha) = - sin (360 ^ ° -alpha) $$ | $$ sin (x) = - sin (2pi-x) $$ |

### For the cosine

You can also find such relationships for the cosine.

**Example:**

$$ cos (30 ^ °) = 0.87 $$ and $$ cos (210 ^ °) = - 0.87 $$.

In general:

Degree | Radians |

$$ cos (alpha) = - cos (180 ^ ° + alpha) $$ | $$ cos (x) = - cos (pi + x) $$ |

And this relationship here:

**Example:**

$$ cos (30 ^ °) = 0.87 $$ and $$ cos (330 ^ °) = 0.87 $$.

This is how it looks in general:

Degree | Radians |

$$ cos (alpha) = cos (360 ^ ° -alpha) $$ | $$ cos (x) = cos (2pi-x) $$ |

*kapiert.de*can do more:

- interactive exercises

and tests - individual classwork trainer
- Learning manager

- How did the UK last so long
- What makes a good bridge round
- How does a compiler generate machine code
- Is my product app a startup?
- Are diatoms immortal
- Can a teacher tape record you
- Only used in business, ceteris paribus
- How do you purchase an iOS app
- What is the cheapest fishing kayak
- How accurate are police radars
- You can remove these grammar doubts
- What is Switzerland best known for?
- Why do vibrating objects make noise?
- What are the best tag suggestion tools
- What are good privacy filter manufacturers
- How do you like history
- What is modesty
- Why did Roman Reigns leave WWE
- What is positive child behavior
- Why can gases change volume
- When were suspension bridges invented?
- What chemicals are in TNT
- How do I combine strength training and fitness
- What is a view start in MVC