Mathers, himself of the WHO, has in criticised countries for compiling poor vital registration statistics [ 8 ]. Still, there was no better worldwide database for analysing suicide and therefore this was chosen as the only source.
While it was rewarding to use national level sources to gain insight into some special cases, it was considered out of the scope of this article to investigate reasons for differences between various sources and possibly also misleading to present different sets of data for the same time periods.
Even so, two datasets were involved in the analysis. The first was prepared by the WHO for to cover all causes of death and maximise inclusion of countries. Data were estimated according to a similar methodology building on population and all-cause mortality estimates, which was used to get and estimates and is described at [ 9 ]. Absolute numbers were available in the WHO database. Proportions of suicides among all injury deaths and suicide rates of different age-groups were computed as well as the male-female rate ratios.
The second dataset was collected by the WHO from individual countries into the WHO Mortality Database to maximise precision of actually measured suicide mortality data and try to achieve comparability across countries.
An overview of latest available data is presented at [ 10 ]. Data by individual countries are presented with 5-year time-intervals starting from at [ 11 ].
The WHO data about gender-specific suicide rates and total numbers, which were available country-by-country, were compiled into an overall table where countries were ranked according to the latest total suicide rate.
Male-female suicide rate ratios were computed. Trend analysis was conducted for all countries and the most characteristic development patterns among those with the highest suicide rates over the past six decades were chosen to be presented in Figure 1 —two countries from Central Europe, two from North Europe, two from the former Soviet Union, and two from Asia.
Suicide rates in selected high-risk countries of the world data were adapted from [ 11 ]. In May the WHO published estimates of deaths by cause for the year , which were based on analysis of latest reported national data on mortality cause distributions as known at the end of The methods used for estimation were briefly explained and the results available online [ 12 ]. Table 1 shows the number of suicides by world region against the background of total mortality and injury mortality in particular.
Suicides i. In all but the European region the amount of road traffic accident casualties prevailed over suicides. Derived from the same database was Table 2 , which shows the estimated distribution of suicides in the world by age-groups and gender. Suicide rate for the world as a whole was estimated at The most clearly outstanding difference between regions was reflected in the male-female rate ratio of suicide—in the European Region it was 4 and in the Americas 3.
Among males in the 15—29 age-group the suicide rate was the highest in the SE Asian region. The lead was tied in the 30—44 age-group but in the 45—59 age-group European males had the highest suicide rate. For ages above 60 males from the Western Pacific region had the highest suicide rate. Females from SE Asia had a remarkably high suicide rate among 15—year-olds and they led also in the next age group.
From age 45 the highest female suicide rates were in the Western Pacific region. Data about latest available suicide rates, which have been measured in individual countries and compiled by the WHO are in Table 3. The leading country was Lithuania with a suicide rate of Also among males the suicide rate was the highest in Lithuania at Among females South Korea with a suicide rate of Male-female rate ratio was the highest in Puerto Rico 6.
Historical data about countries with the highest suicide rates during the past six decades, which are depicted in the Figure 1 , illustrate different paths countries have led regarding the development of the suicide trend [ 11 ].
Sri Lanka, which has had high suicide rates and a very characteristic suicide trend that best illustrates the importance of the availability of means pesticides , would have merited inclusion but due to incompleteness of data in the WHO database, it was ultimately omitted.
The WHO has measured suicide since —shortly after its creation in The list of countries, which have been leading in suicide rate in the world, is not a long one. Japan had the highest rate in the s, Hungary was the top country for the next three decades, and Lithuania took over in the early s for another two decades. Some other countries also deserve to be mentioned.
Although available data are much scarcer before the s, it is plausible to believe that Switzerland has been a world leader in suicide rate because coming into the s its rate was already declining from higher levels in s and s [ 13 ]. Measurement of suicide rate has usually been more difficult in developing economies with less resources. Suicide has been a big issue in Finland and Denmark but even when the rates surpassed 30 per , inhabitants, they were dwarfed by more extreme rates in Hungary at the same time.
Similarly, very high suicide rates in Russia, Latvia, and Estonia were overshadowed by those of Lithuania. In the American region highest rates have been observed in Cuba and more recently in Guyana, which have experienced rates above 20 and 25 per , inhabitants respectively.
Generally the suicide trend has been downward in Europe and there are currently no Western European welfare states in the world top ten for suicide rates. However, a different development has been evident in some other parts of the world—most notably in South Korea where a huge increase has occurred over the last 10 years.
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Microsoft Office C2R V6. Nero Platinum Nitro Pro 11 Lifetime License. The half-angle formulas are as follows:. Given the tangent of an angle and the quadrant in which the angle lies, find the exact values of trigonometric functions of half of the angle.
Using the given information, we can draw the triangle shown in Figure 3. Using the Pythagorean Theorem, we find the hypotenuse to be Then we substitute the value of the cosine we found from the triangle in Figure 3 and simplify.
Now, we will return to the problem posed at the beginning of the section. Another ramp is to be constructed half as steep for novice competition. See Figure 4. Access these online resources for additional instruction and practice with double-angle, half-angle, and reduction formulas. Explain how to determine the double-angle formula for tan 2 x tan 2 x using the double-angle formulas for cos 2 x cos 2 x and sin 2 x.
Explain how to determine two formulas for tan x 2 tan x 2 that do not involve any square roots. For the half-angle formula given in the previous exercise for tan x 2 , tan x 2 , explain why dividing by 0 is not a concern.
Hint: examine the values of cos x cos x necessary for the denominator to be 0. For the following exercises, find the exact values of a sin 2 x , sin 2 x , b cos 2 x , cos 2 x , and c tan 2 x tan 2 x without solving for x. For the following exercises, find the values of the six trigonometric functions if the conditions provided hold.
For the following exercises, simplify to one trigonometric expression. For the following exercises, find the exact value using half-angle formulas. For the following exercises, use Figure 5 to find the requested half and double angles. For the following exercises, simplify each expression. Do not evaluate. For the following exercises, rewrite the expression with an exponent no higher than 1. For the following exercises, reduce the equations to powers of one, and then check the answer graphically.
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