To solve for x, we can use the identity
cos(a - b) = cos(a)cos(b) + sin(a)sin(b)
In this case, a = π/3 and b = x. According to the given formula:
cos(π/3)cos(x) + sin(π/3)sin(x) = 0
Since cos(π/3) = 1/2 and sin(π/3) = √3/2, we get:
(1/2)cos(x) + (√3/2)sin(x) = 0
Multiplying through by 2 to clear fractions gives:
cos(x) + √3sin(x) = 0
Dividing through by cos(x) gives:
tan(x) = -√3
This means that x = arctan(-√3). Solving this in a calculator we get x ≈ -1.047 (in radians).
To solve for x, we can use the identity
cos(a - b) = cos(a)cos(b) + sin(a)sin(b)
In this case, a = π/3 and b = x. According to the given formula:
cos(π/3)cos(x) + sin(π/3)sin(x) = 0
Since cos(π/3) = 1/2 and sin(π/3) = √3/2, we get:
(1/2)cos(x) + (√3/2)sin(x) = 0
Multiplying through by 2 to clear fractions gives:
cos(x) + √3sin(x) = 0
Dividing through by cos(x) gives:
tan(x) = -√3
This means that x = arctan(-√3). Solving this in a calculator we get x ≈ -1.047 (in radians).