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Verizon [17]
3 years ago
15

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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