# cos x

• Jan 12th 2010, 08:34 PM
chil2e
cos x
I would appreciate if someone helps with this problem. Thanks.

Tom and Jerry use their calculators to calculate cos x. Tom enters x as x degrees, while Jerry enters x radians. Tom gets an answer y, while Jerry gets the value -y. Let x be the smallest positive value for which this happens. Find x.
• Jan 12th 2010, 11:55 PM
earboth
Quote:

Originally Posted by chil2e
I would appreciate if someone helps with this problem. Thanks.

Tom and Jerry use their calculators to calculate cos x. Tom enters x as x degrees, while Jerry enters x radians. Tom gets an answer y, while Jerry gets the value -y. Let x be the smallest positive value for which this happens. Find x.

1. Let r denote the value of an angle in radian and d the value of the same angle in degree. Then the conversion of degree into radian is calculated by:

$r = \dfrac d{180} \cdot \pi$

2. If the angle x is measured in degree the cos-function has the property

$\cos(x) =- \cos(180^\circ - x)$

3. According to the text of the question you have to solve the equation for x:

$x = \dfrac{180-x}{180} \cdot \pi$

4. I've got $x \approx 3.087702086...$
• Jan 13th 2010, 12:00 AM
abender
That is a better and more correct approach. Touche.