If rCosx=3 and rSinx=4, find the value of r and x.
(3/r)^2 + (4/r)^2 = 1
25/r^2 = 1
r = ±1/5
tanx = 4/3
x is in QI or QIII
To find the value of r and x, we can use the given equations:
1) rCosx = 3
2) rSinx = 4
Let's solve for r first. Divide equation 1 by equation 2:
(rCosx) / (rSinx) = 3 / 4
Cancel out the common factor, r:
Cosx / Sinx = 3 / 4
Using the identity Tanx = Sinx / Cosx, rewrite the equation:
Tanx = 3 / 4
Now, we can find the value of x by taking the arctan of both sides:
x = arctan(3/4)
Using the inverse tangent function on a calculator, we find:
x ≈ 36.87 degrees (rounded to two decimal places)
Now, substitute this value of x into equation 1 to solve for r:
rCosx = 3
r * Cos(36.87) = 3
Divide both sides by Cos(36.87):
r = 3 / Cos(36.87)
Using a calculator, we find:
r ≈ 3.88 (rounded to two decimal places)
Therefore, the value of r is approximately 3.88 and x is approximately 36.87 degrees.