Question

¿cuál de los siguientes valores de funciones es negativo? a. Sen 120° b. Sen 150° c. Cos 235° d. Cos 300°.

Answer 1

An X-axis and Y-axis rectangular coorganizing system splits the plane in to the four regions recognised as the quadrants. The cross point is indeed the source of the two axes and is made reference to as O. So, the calculation can be defined as follows:

Given:

$\bold{a)\ \sin 120^{\circ}}\\\\\bold{b)\ \sin 150^{\circ}}\\\\\bold{c)\ \cos 235^{\circ}}\\\\\bold{d)\ \cos 300^{\circ}}$

To find:

Find negative function values =?

Solution:

$\therefore \\\\\to \bold{\sin (180- \theta)= \sin \theta} \\\\\to \bold{\cos (180- \theta)= -\cos \theta} \\\\\to \bold{\cos (180+ \theta)= -\cos \theta} \\\\ \to \bold{\cos (360- \theta)= \cos \theta}$

Solve value for a:

$\to \bold{\sin 120^{\circ}= \sin(180-60)}$

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

Solve value for b:

$\to \bold{\sin 150^{\circ}= \sin(180-30)}$

                  $\bold{=\sin 30^{\circ}}\\\\\bold{=\frac{1}{2}}$

Solve value for c:

$\to \bold{\cos 235^{\circ}=-\cos( 180+55)}$

                  $\bold{=- \cos 55^{\circ}}\\\\\bold{= -0.57357643635}}$

Solve value for d:

$\to \bold{\cos 300^{\circ}= \cos(360-60)}$

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

Therefore the final answer is "Option C".

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