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communitycoll
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Homework Statement
How do I find out the exact value of tan^-1 (1 / sqrt(3))?
Homework Equations
nada
The Attempt at a Solution
I don't know where to start.
communitycoll said:Homework Statement
How do I find out the exact value of tan^-1 (1 / sqrt(3))?
Homework Equations
nada
The Attempt at a Solution
I don't know where to start.
communitycoll said:How do I find the angles in the triangle?
communitycoll said:Homework Statement
How do I find out the exact value of tan^-1 (1 / sqrt(3))?
Millennial said:[itex]\frac{1}{\sqrt{3}}=\tan(x)=\frac{\sin(x)}{\cos(x)}[/itex], so it follows from here that [itex]\cos(x)=\sin(x)\sqrt{3}[/itex], and squaring both sides yields [itex]\cos^2(x)=3\sin^2(x)[/itex]. We want to make use of the Pythagorean trigonometric identity, so we replace sine by cosine to get [itex]\cos^2(x)=3-3\cos^2(x)[/itex] which gives [itex]\cos(x)=[/itex].
Your equation is essentially equivalent to this equation. Can you solve this one for x?
An inverse trig function is a mathematical function that undoes a trigonometric function. It takes the output of a trigonometric function and returns the original input value.
The exact value of an inverse trig function is determined by using a calculator or by using a trigonometric table. It is also possible to derive the exact value using mathematical equations and identities.
The main difference between an inverse trig function and a regular trig function is that an inverse trig function takes the output of a trigonometric function as its input and returns the original input value. A regular trig function takes an angle as its input and returns a ratio or value.
Yes, the exact value of an inverse trig function can be irrational, meaning it cannot be expressed as a simple fraction. For example, the exact value of the inverse sine of 0.5 is π/6, which is an irrational number.
Inverse trig functions are used in various fields such as physics, engineering, and navigation to solve problems involving angles and distances. They are also used in computer graphics and animation to create realistic movements and rotations.