Question

What is the arcsecant of 4 and 8?

Answer 1

arcsec 4 = arccos 1/4 = 75.5°
and so on

Answer 2

but 1/4 isn't in the unit circle

Answer 3

so what? trig functions are all about ratios.
Draw a triangle with sides 1,√15 and hypotenuse 4
Then the angle whose secant is 4/1 is the same angle whose cosine is 1/4

Yeah, yeah, you can scale everything so that the hypotenuse is 1, making it lie on the unit circle, but the ratios do not change. The sides are now 1/4, √15/4, and the hypotenuse is 1.

So, the secant is now 1 / (1/4) = 4 as before.

Answer 4

where does √15 come from?

Answer 5

the Pythagorean Theorem.
You clearly did not draw the required right triangle. Don't make me do <u>everything</u>!

Answer 6

cos(4) is same asarccos(1/4). In which 1 is the adjecent and 4 is the hypatanu. the √(4^2-1^2)= √15