Question

find the value of tan 480°​

Answer 1

Given, tan480 ° =tan(5×90 ∘ +30 ∘ )

Here n=5 is odd, so tan changes to cot

=cot(30 ∘ ) since 480 ∘ lies in first quadrant.

$= 1 \div \sqrt{3}$

WHAT IS TAN THETA?

tan theta = sin theta/cos theta (here, theta is an angle) The sine of an angle is equal to the length of the opposite side divided by the length of the hypotenuse side, while the cosine of an angle is the ratio of the adjacent side to the hypotenuse side. Hence, sin x = Opposite Side/Hypotenuse Side.

Answer 2

$\bold{tan480}$

either me can split 480 interns of A and B where A and B are angles which me know

or we can do it by other rule that is 360×n + theta

ok

$\bold{480 - 360 = 120}$

we know trigonometric ratio of 120 so I will proceed with 2nd one

now

$\bold {tan(360 \times 1 + 120)}$

then

$\bold{tan120}$

$\bold{ = - { \sqrt{3} } }$