Cos 3 alpha = - 0.1 solutions in degree
what's the problem?
cos 3θ = -0.1
3θ = cos<su>-1(-.1)
3θ = 95.74°
θ = 31.91°
sorry about the θ -- didn't have an alpha handy.
oops
cos 3θ = -0.1
3θ = cos-1-.1
3θ = 95.74°
θ = 31.91°
you know the cosine is negative in II and III
cos 84.26° = +.1
so 3 alpha = 180 -84.26 or 3alpha = 180+84.26
alpha = 31.9° or 88.1°
You did not state the domain of alpha, I will assume between 0 and 360°
period of cos 3alpha is 360°/3 = 120°
so adding 120 to any answer will yield a new answer
alpha = 31.9 +120 = 151.9
alpha = 151.9+10 = 271.9
alpha = 271.9+120 = 391.9 -- too big
alph = 88.1+120 = 208.1
alpha = 208.1+120 = 328.1
alpha = 31.9, 88.1, 151.9, 208.1, 271.9, and 328.1
To find the solutions for the equation cos(3α) = -0.1 in degrees, you can follow these steps:
1. Start by finding the solutions in radians using the inverse cosine function, cos⁻¹(-0.1). The result will give you the value of 3α in radians.
2. Once you have the value of 3α in radians, divide it by 3 to find the value of α in radians.
3. Finally, convert the radian measure of α to degrees by multiplying it by 180/π.
Let's go through the steps:
1. Use the inverse cosine function on a scientific calculator or math software to find cos⁻¹(-0.1). The result is approximately 1.67096 (radians).
2. Divide 1.67096 by 3 to find the value of α in radians. The result is approximately 0.55699 (radians).
3. Convert the radian measure to degrees by multiplying it by 180/π. The result is approximately 31.915 (degrees).
Therefore, the solutions in degrees for the equation cos(3α) = -0.1 are approximately 31.915 degrees.