Trigonometry Problems - Basics, Advanced & Examples

(ad≥ + 2ycost = coser?t

CA⃡ is the perpendicular bisector of̅BD̅̅̅̅.
Given that AB=3x and AD=4x-1, then what
is the value of x and the hypotenuse?

The area A of a triangle is given by bab sin 0, where a and b are the lengths of two sides and O is the angle between these sides. Suppose that a = 5, b = 10 and 0 = . (a) Find the rate at which A changes with respect to a if b and 0 are held constant. (b) Find the rate at which A changes with respect to 0 if a and b are held constant. (c) Find the rate at which b changes with respect to a if A and O are held constant.

assume a,b starts on the positive x-axis and moves around in a circle. determine a function of a segment from the origin to a point a,b

1. A Harris Interactive survey for InterContinental Hotels & Resorts asked respondents, “When traveling internationally, do you generally venture out on your own to experience culture, or stick with your tour group and itineraries?” The survey found that 23% of the respondents stick with their tour group (USA Today, January 21, 2004).
2. In a sample of six international travelers, what is the probability that two will stick with their tour group?
3. In a sample of six international travelers, what is the probability that at least two will stick with their tour group?
4. In a sample of 10 international travelers, what is the probability that none will stick with the tour group?

sinh(x-y)=Sinhx*coshy-sinhy**coshx

Let ${\displaystyle S_n=\sum _{j=1}^n\sin (\sqrt{j}\pi )}$.

Show $S_{(2M{)}^2}<0$ and $S_{(2M+1{)}^2}>0(M=1,2,3,...)$ .

Triangle ADEF is a Right triangle, where angle F = 90, side d = 19, side f = 38. Find the measure of angle D. Use knowledge of triangles and/or trigonometry to justify your answer.

One of the largest issues in ancient mathematics was accuracy — nobody had calculators that went out ten decimal places, and accuracy generally got worse as the numbers got larger. The famous Eratosthenes experiment, that can be found at famousscientists,org/eratosthenes/, relied on the fact known to Thales and others that a beam of parallels cut by a transverse straight line determines an equal measure for the corresponding angles. Given two similar triangles, one with small measurements that can be accurately determined, and the other with large measurements, but at least one is known with accuracy, can the other two measurements be deduced? Explain and give an example. 
The similarity of triangles gives rise to trigonometry. 

How could we understand that the right triangles of trigonometry with a hypotenuse of measure 1 represent all possible right triangles? Ultimately, the similarity of triangles is the basis for proportions between sides of two triangles, and these proportions allow for the calculations of which we are speaking here. The similarity of triangles is the foundation of trigonometry.

One of the largest issues in ancient mathematics was accuracy-nobody had calculators that went out ten decimal places, and accuracy generally got worse as the numbers got larger. The famous Eratosthenes experiment. Given two similar triangles, one with small measurements that can be accurately determined, and the other with large measurements, but at least one is known with accuracy, can the other two measurements be deduced? Explain and give an example. The similarity of triangles gives rise to trigonometry. 
How could we understand that the right triangles of trigonometry with a hypotenuse of measure 1 represent all possible right triangles? Ultimately, the similarity of triangles is the basis for proportions between sides of two triangles, and these proportions allow for the calculations of which we are speaking here. The similarity of triangles is the foundation of trigonometry.