In the summer, St. Petersburg, Russia, has many more daylight hours than St. Petersburg, Florida (United States), because of their locations with respect to the equator. From late May to early July, nights are bright in St. Petersburg, Russia. The nature of the white nights can be explained by the geographical location of St. Petersburg in Russia. It is one of the world’s most northern cities: located at 59°57′ north (approximately the same latitude as Seward, Alaska). Due to such a high latitude, the sun does not go under the horizon deep enough for the sky to get dark.
Trigonometric equations can be used to represent the relationship between the number of daylight hours and the latitude of the city. Inverse trigonometric functions allow us to find the latitude given the number of hours of sunlight.
IN THIS CHAPTER, we first develop the inverse trigonometric functions and then use these to assist us in solving trigonometric equations. As with all equations, the goal is to find the value(s) of the variable that make the equation true. You will find that trigonometric equations (like algebraic equations) can have no solution, one or more solutions, even an infinite number of ...
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