So how do find the arcsec(-3)?
secy = x
secx = -3
1/cosx = -3
1 = -3cosx
-1/3 = cosx
Now what angle is this?
by arcsec(-3) you are looking for an angle Ø so that
secØ = -3
or
cosØ = -1/3
we know that the cosine is negative in quads II and III
so Ø = 180° - 70.53° OR Ø = 180° + 70.53°
Ø = appr 109.5° or appr. 250.5°
I had my calculator set to degrees, if you need radians, set it to that, then
find 2ndF cos (/13) to get 1.91..
and it to and subtract it from π for the two answers in radians.
small typo:
2ndF cos (/13) should have been 2ndF cos (1/3)
To find the angle whose secant is -3, you can use the inverse trigonometric function called arcsecant (arcsec), which gives you the angle whose secant is a given value.
In this case, you have sec(x) = -3. To use the arcsec function, you need to find the value of x. Starting from the equation:
1 = -3cos(x)
You can isolate cos(x) by dividing both sides of the equation by -3:
-1/3 = cos(x)
Now, to find the angle whose cosine is -1/3, you would use the inverse cosine function (arccos), not the arcsec function. The arccos function gives you the angle whose cosine is a given value, whereas the arcsec function gives you the angle whose secant is a given value.
Using the arccos function, you can find the angle whose cosine is -1/3. You can do this by taking the inverse cosine of -1/3.
arccos(-1/3) ≈ 109.47 degrees or ≈ 2.034 radians
So, the angle whose cosine is -1/3 is approximately 109.47 degrees or 2.034 radians.