SOLUTION: Find each of the following exactly in radians and degrees. Do not use a calculator. cot-1(√3/3)
Algebra.Com
Question 825935: Find each of the following exactly in radians and degrees. Do not use a calculator. cot-1(√3/3)
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
When a problem says "find the exact value" or "do not use a calculator" it usually means that the problem involves special angles.
Here's a solution:- With the hint of "do not use a calculator", we should look into the special angle values for cot when we see .
- It should not take long to find that a reference angle of has a cot value of .
- Since the angle in question, , has a positive cot value and since cot is positive in the 1st and 3rd, we now know that terminates in one of these quadrants.
- We should know that the inverse cot function has a range limited to angles between 0 and . So will have a value in that range. (Note: This range includes angles which terminate in the 1st quadrant (between 0 and ) and the 2nd quadrant (between and ).
- Combining the fact that the angle must terminate in the 1st or 3rd quadrants (because the cot is positive) and the range of the inverse cot function, we should now know that is between 0 and
- Combining that with the fact that the reference angle is , it should not take long to figure out that:
is the only angle with the right reference angle for a cot of , with a positive sin and in the range of the inverse cot function.
To turn this into degrees, just multiply it by .
P.S. There is what appears to be a multiplication symbol between the exponent and the argument of cot. Ignore it. Do not use it yourself. It should not be there. It is just a flaw in algebra.com's formula drawing software.
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