Solving Trigonometric Problems: Exploring Sine, Cosine & Tangent

[praveenpp]

hi every one,

i have one doubt i studied abt trignomentry. there finding the triangle angle or side of the triangle using sine function. if we are taking right angle triangle sine A = opp/hypo, cos A = adj/hypo and tan A=opp/adj. here we are finding angle for A only why we are having three formulas what is the use for that?. and how we are finding sin A. what is the procedure behind that for ex: sin 90 = 1 how this ans come? Pls anybody reply me.

 

[Angry Citizen]

why we are having three formulas what is the use for that?

There are more than three formulas. There are six major ones, which are sine, cosine, and tangent, and the reciprocal identities cosecant, secant, and cotangent (respectively). Cosine and sine represent the x and y values (respectively) of a point that lies on a circle whose radius is exactly equal to the hypotenuse line formed by the unique opposite and adjacent lines required to form the trigonometric values. Tangent represents the slope of the hypotenuse. All six functions become very useful when you are studying calculus. For instance, if I were to take the derivative of the tangent function, I would write sec^2(x), which is the same as 1/cos^2(x). Or if I wanted to find the derivative of the sine function, I would write cos(x). Sine and cosine are absolutely essential to any serious, in-depth study of trigonometry.

how we are finding sin A. what is the procedure behind that for ex: sin 90 = 1 how this ans come?

In the old days, mathematicians would copy down tables of trig values for as many angles as they could. They did this by using the identities of the trig functions. For instance, if they wanted to find out what sin(pi/4) was, they would construct a triangle whose opposite and adjacent sides were equal, and then divide the opposite by the resultant hypotenuse.

Nowadays, we have calculators with algorithms for that. Thank goodness! Now we only have to memorize the values for pi/3, pi/4, pi/6, and pi/2.

 

[CRGreathouse]

And don't forget the versine, the hacovercosine, the exsecant... thank goodness I'm not an olden-days sailor.

 

[praveenpp]

thnks for reply

 

[CellCoree]

I would like to explain the use and procedure behind the three trigonometric formulas for finding the angle and sides of a right triangle. The sine, cosine, and tangent functions are used to solve problems involving right triangles, where one angle is 90 degrees. These functions are based on the relationship between the sides of a right triangle and the angles within it.

The sine function, as you mentioned, is defined as the ratio of the length of the side opposite the given angle (called the opposite side) to the length of the hypotenuse (the longest side of the triangle). This can be expressed as sin A = opp/hypo. The cosine function is defined as the ratio of the length of the side adjacent to the given angle (called the adjacent side) to the length of the hypotenuse, which can be written as cos A = adj/hypo. Finally, the tangent function is defined as the ratio of the length of the side opposite the given angle to the length of the side adjacent to it, or tan A = opp/adj.

So, why do we have three formulas for finding the same angle? The reason is that each formula is useful in different scenarios. For example, if we know the length of the opposite and hypotenuse sides, we can use the sine function to find the angle. If we know the length of the adjacent and hypotenuse sides, we can use the cosine function. And if we know the length of the opposite and adjacent sides, we can use the tangent function. Each formula provides a different perspective on the triangle and allows us to solve a variety of problems.

Now, let's address your question about finding the value of sin 90 degrees. This value is a special case because it corresponds to the angle of 90 degrees, which is the maximum angle in a right triangle. In this case, the opposite side is equal to the length of the hypotenuse, so sin 90 degrees becomes 1, as you correctly stated. This is because the ratio of the opposite side to the hypotenuse is 1/1, which simplifies to 1. This is just one example of how the trigonometric functions can be used to solve problems involving right triangles.

I hope this explanation helps to clarify the use and purpose of the trigonometric functions in solving problems involving right triangles. They are powerful tools that allow us to understand and analyze the relationships between the sides and angles of