what are the values of theta in the interval 0 degrees is lessthan or equal to theta is less than or equal to 360 degrees that satisfy the equation tan theta minus square root of 3 equals 0?
tan theta - sqrt3 = 0, therefore
tan theta = sqrt 3
One such angle is 60 degrees.
The other one is in the third quadrant, 60 degrees from the theta = 180 sdegrees line. That would make it 240 degrees.
To find the values of theta that satisfy the equation tan(theta) - √3 = 0 in the interval 0° ≤ θ ≤ 360°, you need to solve the equation for theta.
Step 1: Start with the given equation: tan(theta) - √3 = 0.
Step 2: Add √3 to both sides of the equation to isolate tan(theta):
tan(theta) = √3.
Step 3: Take the inverse tangent (arctan) of both sides to find the value of theta:
theta = arctan(√3).
Step 4: Use a calculator to find the inverse tangent of √3. The exact value is 60°, which is the same as π/3 in radians.
Hence, the values of theta in the interval 0° ≤ θ ≤ 360° that satisfy the equation tan(theta) - √3 = 0 are θ = 60° and θ = 240°.
Please note that tangent is a periodic function, so it repeats every 180° (or π radians) in this interval. To find all solutions, you can add multiples of 180° (or π radians) to the initial solutions.