Yeah, you can substitute,Tyrion101 said:I work a good deal better when the equation is in x and y form, is it possible to set up a trig expression like 5Cos(x)/(Sin(x)-1)and substitute the proper x or y equivalent so long as I remember to replace the trig identities later when the problem is finished? Or can you just not solve these problems like this?
By ``proper x or y equivalent'' do you mean the types of definitions for sine and cosine we commonly attach to their definitions from triangles or unit circles? I' not sure what you're meaning is, or of the type of problem you are intending to solveTyrion101 said:I work a good deal better when the equation is in x and y form, is it possible to set up a trig expression like 5Cos(x)/(Sin(x)-1)and substitute the proper x or y equivalent so long as I remember to replace the trig identities later when the problem is finished? Or can you just not solve these problems like this?
The value of a trigonometric function in terms of x, y, and r can be found by using the Pythagorean theorem and the definition of the trigonometric functions. For example, the sine function can be written as sin(x) = y/r, where x is the angle, y is the opposite side, and r is the hypotenuse of a right triangle.
The trigonometric functions (sine, cosine, and tangent) are ratios of the sides of a right triangle. The sine function is equal to the ratio of the opposite side to the hypotenuse, the cosine function is equal to the ratio of the adjacent side to the hypotenuse, and the tangent function is equal to the ratio of the opposite side to the adjacent side.
To find a missing side length in a right triangle, use the trigonometric functions and the given angle to set up a ratio between the known side length and the unknown side length. Then, solve the equation for the unknown side length by using algebraic manipulation.
Yes, trigonometric functions can have negative values. The sign of a trigonometric function depends on the quadrant in which the angle lies. In the first and third quadrants, all trigonometric functions are positive. In the second and fourth quadrants, only the sine and cosecant functions are positive.
Trigonometric functions are used in various fields, such as engineering, physics, and mathematics, to model and solve real-world problems. They are used to calculate distances, angles, and forces in structures, to analyze motion and waves, and to model natural phenomena such as sound and light waves.