- #1
anemone
Gold Member
MHB
POTW Director
- 3,883
- 115
Find the smallest natural number $n$ for which $\sin \left(\dfrac{1}{n+1934}\right)<\dfrac{1}{1994}$.
for (unsigned int n = 0; n <= 60; n++)
if ((sin(1/(n + 1934.0))) < 1/1994.0)
std::cout << n;
[sp]anemone said:Find the smallest natural number $n$ for which $\sin \left(\dfrac{1}{n+1934}\right)<\dfrac{1}{1994}$.
A trigonometric inequality is an inequality that involves trigonometric functions, such as sine, cosine, and tangent.
This inequality means that the value of sine of 1 divided by n plus 1934 is less than 1 divided by 1994.
To solve a trigonometric inequality, you need to use algebraic techniques and the properties of trigonometric functions to isolate the variable and determine its possible values.
If the inequality is true for all values of n, then it means that the statement is always true, regardless of the value of n. In other words, there are no values of n that make the inequality false.
You can check your solution by plugging in different values for n into the original inequality and seeing if the inequality holds true for each value. You can also graph the inequality and see if your solution falls within the shaded region.