Question

Evaluate the sin, cos and tan for 120deg without using a calculator

Answer 1

Using equivalent angles, we have that the measures are given as follows:

• $\sin{120^\circ} = \frac{\sqrt{3}}{2}$

• $\cos{120^\circ} = -\frac{1}{2}$

• $\tan{120^\circ} = -\sqrt{3}$

What are equivalent angles?

Each angle on the second, third and fourth quadrants will have an equivalent on the first quadrant.

120º is in the second quadrant, hence the equivalent on the first quadrant is:

180º - 120º = 60º.

The sine on the second quadrant is positive, hence:

$\sin{120^\circ} = \sin{60^{\circ}} = \frac{\sqrt{3}}{2}$

The cosine on the second quadrant is negative, hence:

$\cos{120^\circ} = \cos{60^{\circ}} = -\frac{1}{2}$

The tangent is given by the sine divided by the cosine, hence:

$\tan{120^\circ} = \frac{\sin{120^\circ}}{\cos{120^\circ}} = -\sqrt{3}$

More can be learned about equivalent angles at brainly.com/question/24787111

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