Thread re-opened for some questions...Einstein's Cat said:
It is self- study maths and thank you for the adviceberkeman said:
Why don't you read the LaTeX tutorial, and then show us the equation that you are asking about in LaTeX form. Then also show us what steps you think might be useful for trying to manipulate the equation to isolate the variable you want. Please always show your best efforts when asking questions here at the PF.Einstein's Cat said:
Since it is for self-study, it is schoolwork-like. So I will move the thread to the Homework Help forums, where such threads should go.Einstein's Cat said:
A pretty obvious answer is that [itex]b= Sin(90- Sin^{-1}(a))[/itex] but that probably isn't what you want-surely you saw that..Einstein's Cat said:
That is indeed what I was wanting and so thank you very much for I am completely ignorant of rearranging sin functions in algebraic termsHallsofIvy said:
But you can simplify it much more, getting rid of the trig functions entirely.Einstein's Cat said:
I believe Sin(90) is equal to 1haruspex said:
Yes, but that doesn't help. Consider a right-angled triangle. Let x be one of the other angles. What is the third angle?Einstein's Cat said:
The other angle would equal 180 -(90+x) and I'm sorry but I do not know the answer to your final questionharuspex said:
Consider a triangle ABC. Angle at C is a right angle, so AB is the hypotenuse. Consider angle at A. The sine of A is the ratio of two sides of the triangle. Which two sides? Which ratio is the cosine?Einstein's Cat said:
The sine function, denoted as sin(x), is a mathematical function that represents the ratio of the side opposite an angle in a right triangle to the hypotenuse. In equations, it is used to model periodic phenomena, such as waves or oscillations, and to find unknown angles or side lengths in triangles.
The sine function, sin(x), takes an angle as its input and outputs the ratio of the opposite side to the hypotenuse. The inverse sine function, sin⁻¹(x) or arcsin(x), takes a ratio as its input and outputs the angle that produces that ratio in a right triangle. In other words, the inverse sine function "undoes" the sine function.
To graph a sine function, you can plot points by choosing values for the angle (x-value) and calculating the corresponding value of sin(x) (y-value). These points can then be connected to create a smooth, periodic curve. Alternatively, you can use a graphing calculator or online graphing tool to plot the graph automatically.
The sine function has several key properties, including being a periodic function with a period of 360 degrees or 2π radians, having a maximum value of 1 and a minimum value of -1, and being an odd function (sin(-x) = -sin(x)). It also has an inverse function, the inverse sine function, and is one of the three basic trigonometric functions, along with cosine and tangent.
The sine function has many real-life applications, such as in music and sound waves, where it is used to model the vibrations of strings and air molecules. It is also used in physics to describe the motion of pendulums, springs, and other oscillating systems. Additionally, it is used in engineering and architecture to calculate angles and distances in structures and design curves in roads and bridges.