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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