What is the arcsecant of 4 and 8?
arcsec 4 = arccos 1/4 = 75.5°
and so on
but 1/4 isn't in the unit circle
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.
where does √15 come from?
the Pythagorean Theorem.
You clearly did not draw the required right triangle. Don't make me do everything!
cos(4) is same asarccos(1/4). In which 1 is the adjecent and 4 is the hypatanu. the √(4^2-1^2)= √15
The arcsecant function, denoted as arcsec(x), is the inverse function of the secant function. It gives us the angle whose secant is equal to a given value.
To find the arcsecant of a value, we need to use a scientific calculator that has the arcsecant function or refer to a trigonometric table. Let's calculate the arcsecant of 4 and 8 using a calculator:
1. Enter the value 4 into a calculator.
2. Press the "2nd" or "Shift" button (usually located near the bottom-left corner of scientific calculators).
3. Then press the "sec" button. This will give you the secant of 4.
4. Lastly, press the "inv" or "arcsec" button to find the arcsecant of 4.
Repeat the same steps to find the arcsecant of 8.
Note that the arcsecant function returns an angle in radians. If you need the answer in degrees, you can convert it by multiplying the radian value by (180/π).
Please note that the arcsecant function is only defined for values that are greater than or equal to 1 or less than or equal to -1. So, if you try to find the arcsecant of a number outside this range, you will get an error.