# What is the value of sin150

### 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) \$\$

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