Hey :)
I was wondering if someone could tell me if this answer and working is correct or not...
Cos theta =-0.25
Cos inverse -0.25 = -14
therefore theta equals:
180--14=194or/and
180+-14=166
Any help would be much appreciated :)
Thanks!
cos (theta) = -0.25
theta = cos^-1 (-0.25)
there are two answers:
theta = 104.48 degrees = 3.65 radians
and,
theta = -104.48 degrees = -3.65 radians
hope this helps~ :)
Usually the required angles are in the domain of
0 ≤ Ø ≤ 360°
Since the given cosØ is negative, by the CAST rule,
Ø must be in either quadrant II or III
from cosØ = +.25 we get the reference angle of 75.52°
so Ø = 180°-75.52° or 104.48° (Jai's answer)
or Ø = 180°+75.52° or 255.52°
Since the period of cosØ is 360°, you can get other answers by adding or subtracting multiples of 360°
(For Jai's second answer, 255.52 - 360° = 104.48°)
I have no idea how you came up with
inverse cos (-.25) = -14
Hello! Let's check if the calculations are correct.
First, you have given that cos(theta) = -0.25.
To find theta, you need to take the inverse cosine (also known as the arccosine) of -0.25. This can be denoted as cos^(-1)(-0.25) or acos(-0.25).
Calculating the inverse cosine of -0.25 in degrees can be done using a scientific calculator or by looking it up in a trigonometric table.
Upon calculating, the exact value of cos^(-1)(-0.25) is approximately 104.48 degrees (rounded to two decimal places).
Now let's analyze your working:
1. You wrote cos inverse of -0.25 as -14. This seems to be an error, as the value should be around 104.48 degrees, not -14.
2. Then you continued your calculation by subtracting 180 from -14, which resulted in 194 degrees.
3. Additionally, you added 180 to -14, which gave you 166 degrees.
Both of these steps seem unclear in terms of the reasoning behind them.
To summarize, your initial working is not entirely correct.
To find theta, use the inverse cosine function (cos^(-1)) on -0.25, which gives approximately 104.48 degrees. There is no need to subtract or add 180 in this case.
I hope this clarifies things for you! If you have any further questions, feel free to ask.