They call it Trigonometry?

Geometry Level 3

If $\tan 64 = 2.050$

then, find the value of $\tan 65$ .

Note:

1)All the angles given in the question are in degrees.

2)Think creatively, please don't use a calculator.

The answer is 2.144.

2 solutions

Vignesh S
Apr 21, 2016

Use errors and approximations used in calculus. $\Delta y = \dfrac{d(\tan(x))}{dx}*\Delta x$ $\Delta x=1°, x=64°,y=\tan(x)+\Delta y$ Then substitute the values. The error is in $3rd$ decimal place.

Guilherme Niedu
Apr 15, 2016

One possible solution is the approximation $\tan(x) \approx x$ if $x \rightarrow 0$

Since $1º$ in radians is $\frac{\pi}{180} = 0.01745$ , we can use formula for the tangent of the sum and this approximation to get:

$\tan(64º) = \frac{2.050 + 0.01745}{1 - 2.050\cdot 0.01745} = 2.144$

Another thing that you can do is to find value of $\tan(32^{\circ})$ , $\tan(16^{\circ})$ , $\tan(8^{\circ})$ , $\tan(4^{\circ})$ , $\tan(2^{\circ})$ and $\tan(1^{\circ})$ by half angle identity. Then you casn find the value of $\tan(65^{\circ})$ by angle sum identity.

However this method is very long and clumsy.

Akshay Yadav - 5 years, 2 months ago

They call it Trigonometry?

The answer is 2.144.

2 solutions

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