Question

What are the six trig function values of `420`?

Answer 1

Please read the explanation.

Explanation:

What are the six trigonometric function values of `color(red)(420^@`?

Given:

Angle `theta = 420^@`

We must find

`sin(420^@), cos(420^@), tan(420^@), csc(420^@), sec(420^@), and cot(420^@)`

Reference Angle is the angle measure from terminal side to x-axis.

Hence, reference angle is `60^@`

It falls in the I quadrant where in all the six trigonometric functions are positive. as seen from the chart below.

Special Right Triangle with `color(red)(30^@-60^@-90^@`

Now, we can write our six trigonometric functions:

`sin(420^@) = sqrt(3)/2`

`cos(420^@) = 1/2`

`tan(420^@) = sqrt(3)/1 or sqrt(3)`

`csc(420^@) = 2/sqrt(3) or (2sqrt(3))/3`

`sec(420^@) = 2/1 or 2" "`and

`cot(420^@) = 1/sqrt(3) or sqrt(3)/3`

Hope it helps.