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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.
Consider the right triangle with a hypotenuse of 2 and one side equal to √3. What are the angles in this triangle?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.
What's the third side in the right triangle?How do I find the angles in the triangle?
This is one of the 'special' triangles, for which we know exact trigonometric ratios. Look at the 60°-30°-90° triangle for the answer. The point of the problem is to solve the question without using a calculator, only the special triangle.Homework Statement
How do I find out the exact value of tan^-1 (1 / sqrt(3))?
Wow, that's the very long way around :) Though elegant, you can avoid all of this by simply looking at a 30-60-90 triangle and choosing the angle whose [itex] \tan^{-1} = \frac{1}{sqrt(3)} [/itex][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?