Cot( theta) -1=0
1/Tan(theta)-1 = 0
1/Tan(theta) = 1
Tan(theta) = 1
theta = 45 deg.
Are we solving?
cot Ø = 1
or
tanØ = 1
angle in standard position is 45° or π/4 rads
the tangent is positive in I or III
Ø = 45° or 225°
or
Ø = π/4 or 5π/4
To solve the equation cot(theta) - 1 = 0, we need to find the values of theta that make the equation true. Let's break it down into steps:
Step 1: Rewrite the equation
cot(theta) - 1 = 0
Step 2: Solve for cot(theta)
cot(theta) = 1
Step 3: Find the angle whose cotangent is 1
The cotangent of an angle is equal to the adjacent side divided by the opposite side in a right triangle. When the cotangent is 1, it means that the adjacent side and opposite side have the same length.
Step 4: Determine the reference angle
Since the cotangent is positive, the angle must lie in either the first or third quadrant. To find the reference angle, we can take the inverse cotangent (also known as arccot) of 1.
Reference angle = arccot(1)
Step 5: Calculate the reference angle
Using a calculator, the arccot(1) equals π/4 or 45 degrees.
Step 6: Find the solutions
Since cotangent is positive in both the first and third quadrants, we can find the solutions by adding or subtracting 180 degrees or π radians.
The solutions to the equation cot(theta) - 1 = 0 are:
theta = π/4 + kπ, where k is an integer.
Note: It's important to be cautious when dealing with trigonometric functions and their inverses. Make sure your calculator is set to the correct degree or radian mode for accurate results.