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[tex]\[ \sin \left(90^{\circ}-x\right)=-\frac{\sqrt{3}}{2} \][/tex]

The value of [tex]\( x \)[/tex] that satisfies the equation is

Sagot :

GinnyAnswer
Let's solve the given trigonometric equation step-by-step.

1. Understand the given equation:
[tex]\[\sin \left(90^{\circ} - x\right) = -\frac{\sqrt{3}}{2}\][/tex]

2. Use the co-function identity for sine:
Recall that [tex]\(\sin \left(90^{\circ} - x\right) = \cos(x)\)[/tex]. This allows us to rewrite the given equation in terms of cosine:
[tex]\[\cos(x) = -\frac{\sqrt{3}}{2}\][/tex]

3. Determine the angles where [tex]\(\cos(x) = -\frac{\sqrt{3}}{2}\)[/tex]:
The values of [tex]\(x\)[/tex] for which [tex]\(\cos(x) = -\frac{\sqrt{3}}{2}\)[/tex] are known from the unit circle. These angles are:
- [tex]\( 150^{\circ} \)[/tex] (since [tex]\( \cos(150^{\circ}) = -\frac{\sqrt{3}}{2} \)[/tex])
- [tex]\( 210^{\circ} \)[/tex] (since [tex]\( \cos(210^{\circ}) = -\frac{\sqrt{3}}{2} \)[/tex])

Therefore, the value of [tex]\(x\)[/tex] that satisfies the equation is:
[tex]\[ \boxed{150^{\circ}\ \text{and}\ 210^{\circ}} \][/tex]
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