Question

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

Answer 1

A function of the form $f(x) = x^{-n}$, wherein n is a natural number, is regarded as a negative power function. Inside the form, we might also put $f(x)$,that is$f(x) = \frac{1}{x^n}$,and the further calculation can be defied 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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