Approximate, to the nearest 0.1∘, all angles θ in the interval [0∘,360∘) that satisfy the equations. If there are no solutions, enter DNE
tan(θ)=−2.3415
my answers
113.13, (180-66.87)
293.13 (360-66.87)
thanks
check my work please
looks good to me
oobleck...the computer said wrong...What could I possibly be doing wrong?
thanks
never mind...i got it...it wanted me to drop the 3 at the end
thanks oobleck
To find the values of θ that satisfy the equation tan(θ) = -2.3415, we can use the inverse tangent function (also known as arctan) to solve for θ.
Step 1: Calculate the angle whose tangent is -2.3415
Using a calculator that has the inverse tangent function, enter -2.3415 and find its inverse tangent. This can also be written as arctan(-2.3415) or tan^(-1)(-2.3415). The calculated value is approximately -66.87°.
Step 2: Find all angles in the interval [0°, 360°) that satisfy the equation
In the given interval, we need to find the angles where the tangent is equal to -2.3415. We have already found one solution, which is -66.87°.
To find the other solutions, we can add or subtract multiples of 180° from the known solution, -66.87°, until we get within the given interval [0°, 360°).
Adding 180° to -66.87°:
-66.87° + 180° = 113.13°
Subtracting -66.87° from 360°:
360° - 66.87° = 293.13°
So, the approximate values of θ that satisfy the equation tan(θ) = -2.3415 in the interval [0°, 360°) are approximately 113.13° and 293.13°.
Your answers of 113.13° and 293.13° are correct based on the given equation and interval.