what are the values of the angle in the interval 0<the angle<360 that satisfy the equation tan beta- radical 3=o
tanx - √3 = 0
tanx = √3
At this point it helps to have memorized the trig ratios for the few angles where at least one of them is rational. In this case, recall that
sin60° = √3/2
cos60° = 1/2
tan60° = √3
Then recall that tanx >0 in QI,QIII
To find the values of the angle in the interval 0 < θ < 360 that satisfy the equation tan β - √3 = 0, we can use inverse trigonometric functions.
Step 1: Add √3 to both sides of the equation.
tan β = √3
Step 2: Use the inverse tangent function to find the angle.
β = arctan(√3)
Step 3: Calculate the value of arctan(√3).
On most calculators, you can use the "tan^-1" or "atan" button to find the inverse tangent. In this case, arctan(√3) is approximately 60 degrees.
Step 4: Since the range of inverse tangent is -90 degrees to 90 degrees, we need to find the values of β in the interval 0 < β < 360.
The angle β = 60 degrees satisfies the equation tan β - √3 = 0 within the given interval.
Therefore, the only value of β in the interval 0 < β < 360 that satisfies the equation is β = 60 degrees.