Given tan 0 = -5/12 determine the possible values of 0 to the nearest hundreth
So what I did is find that tan-1(5/12) equals 0.35. Then because tan can be negative in quadrants 1 and 3 subtract 0.35 from pi and then from 2pi.
So I got 2.79 and 5.933 I'm not sure if this is right or not though
tan is negative in quads II and IV
but your numbers seem right?
tan^-1(5/12) = .3948
check your math
Your approach is correct! To find the possible values of θ (denoted as 0 in your question), you correctly used the inverse tangent function (tan^-1) to solve for θ. Let's go through the steps again to confirm your answer:
Given tan 0 = -5/12, you found that tan^-1(5/12) ≈ 0.35.
Since the tangent function can be negative in quadrants I and III, we need to consider both positive and negative values of 0. To obtain the positive value, we don't need to make any adjustments to 0.35.
For the negative value, we subtract 0.35 from π (180 degrees) to get the value in quadrant III. So, π - 0.35 ≈ 2.79.
Now, let's find the value in quadrant I by adding 0.35 to 2π (360 degrees). This gives us 2π + 0.35 ≈ 6.28 + 0.35 ≈ 5.93.
Therefore, the possible values of 0 to the nearest hundredth are approximately 0.35, 2.79, and 5.93.
Your answer of 2.79 and 5.933 (rounded to three decimal places) is indeed correct!