How do you find the exact value of tan 405 degrees?

Question

How do you find the exact value of tan 405 degrees?

1 Answer

Impact of this question

17755 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-06-11T18:06:57

$tan 405 = 1$ $tan405=1$

Explanation:

On the unit circle, the nearest $x$ $x$ -axis to $405$ $405$ degrees is $360$ $360$ degrees. This means the reference angle (difference between the two) is $45$ $45$ degrees.

What do we know about $45$ $45$ degrees?

The coordinates are $(\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2})$ $(sqrt2/2,sqrt2/2)$

where the $x$ $x$ coordinate is the $cos$ $cos$ value and the $y$ $y$ coordinate is the $sin$ $sin$ value. We understand $tan θ$ $tantheta$ to be defined as

$\frac{sin θ}{cos θ}$ $sintheta/costheta$

Thus, we have $\frac{\frac{\sqrt{2}}{2}}{\frac{\sqrt{2}}{2}}$ $(sqrt2/2)/(sqrt2/2)$ , which simplifies to $1$ $1$ .

We found $tan 45$ $tan45$ , which is the same as $tan 405$ $tan405$ because $45$ $45$ degrees is its reference angle.

$tan 405 = 1$ $tan405=1$

Hope this helps!

Science

Math

Humanities

... and beyond

How do you find the exact value of tan 405 degrees?

1 Answer

Explanation:

Related questions

Impact of this question