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3 years ago

What is the exact value of sin(π/6) and tan(π/4)?

Mathematics

2 answers:

g100num [7]3 years ago

3 0

Sin (pi/6) = 1/2
Tan (pi/4) is 1.
If you need to know why, leave me a comment!

malfutka [58]3 years ago

3 0

Answer:

The exact value of $Sin(\frac{\pi}{6} )=\frac{1}{2}$ and $tan(\frac{\pi}{4})=1$

Step-by-step explanation:

Consider the Special right angle $30^{\circ} - 60^{\circ} -90^{\circ}$ triangle as shown in the attachment.

The ratio of its sides are $1:\sqrt{3}:2$ as shown in figure. The smallest side, opposite the $30^{\circ}$ angle, is 1. The side opposite the angle $60^{\circ}$ is $\sqrt{3}$ . The longest side, i.e the hypotenuse is 2.

Therefore, any triangle of $30^{\circ} - 60^{\circ} -90^{\circ}$ will have its side in their ratios.

To find the exact value of $Sin(\frac{\pi}{6})$ .

By definition;

$Sine=\frac{Perpendicular}{Hypotenuse}$

From the figure and by definition of sine:

$Sin(\frac{\pi}{6} )=\frac{1}{2}$

Therefore, the exact value of $Sin(\frac{\pi}{6} )=\frac{1}{2}$ .

Now, to find the exact value of $tan(\frac{\pi}{4})$

For this , we have special right angle $45^{\circ}-45^{\circ}-90^{\circ}$ triangle, as shown in the attachment.

The ratio of its sides are $1:1:\sqrt{2}$ .

By definition of tangent,

$tan=\frac{Perpendicular}{Base}$

From the figure, we have

$tan(\frac{\pi}{4}) =\frac{1}{1} =1$

Therefore, the exact value of $tan(\frac{\pi}{4})=1$

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