https://r2.erweima.ai/mathbot/image/1724607415943695kxfbb.jpg

Os pontos 
\[A\], 
\[B\] e 
\[C\] pertencem ao círculo trigonométrico.
Um círculo trigonométrico em um plano cartesiano x y. O centro do círculo trigonométrico está na origem e a circunferência do círculo toca (um, zero), (zero, um), (um negativo, zero) e (zero, um negativo). O ponto A está localizado perto das três horas no círculo. O ponto B está localizado perto das doze horas no círculo. O ponto C está localizado perto das nove horas no círculo.
\[y\]
\[x\]
\[A\]
\[B\]
\[C\]
\[\small 1\]
\[\small 1\]
\[\small{-1}\]
\[\small{-1}\]
Qual das coordenadas é igual a 
\[\cos\left(\pi\right)\]?
Escolha 1 resposta:
Escolha 1 resposta:
(Escolha A)   A coordenada de 
\[x\] do ponto 
\[A\]
A
A coordenada de 
\[x\] do ponto 
\[A\]
(Escolha B)   A coordenada de 
\[y\] do ponto 
\[A\]
B
A coordenada de 
\[y\] do ponto 
\[A\]
(Escolha C)   A coordenada de 
\[x\] do ponto 
\[B\]
C
A coordenada de 
\[x\] do ponto 
\[B\]
(Opção D, verificada)   A coordenada de 
\[y\] do ponto 
\[B\]
D
A coordenada de 
\[y\] do ponto 
\[B\]
(Escolha E)   A coordenada de 
\[x\] do ponto 
\[C\]
E
A coordenada de 
\[x\] do ponto 
\[C\]
(Escolha F)   A coordenada de 
\[y\] do ponto 
\[C\]
F
A coordenada de 
\[y\] do ponto 
\[C\]

The image shows a unit circle on the coordinate plane with points \(A\), \(B\), and \(C\) marked on it. The unit circle intersects the \(x\)- and \(y\)-axes at four key points: \((1, 0)\), \((0, 1)\), \((-1, 0)\), and \((0, -1)\).

### Analyzing the Coordinates of Points \(A\), \(B\), and \(C\) on the Unit Circle:

1. **Point \(A\)** is located on the positive \(x\)-axis, at \((1, 0)\).
2. **Point \(B\)** is located on the positive \(y\)-axis, at \((0, 1)\).
3. **Point \(C\)** is located on the negative \(x\)-axis, at \((-1, 0)\).

### Solving the Question:

The question asks which of these coordinates is equal to \(\cos(\pi)\).

- The cosine function \(\cos(\theta)\) for an angle \(\theta\) represents the \(x\)-coordinate of a point on the unit circle corresponding to that angle.
- For \(\theta = \pi\) (which is 180 degrees), the point on the unit circle is \((-1, 0)\) because at \(\pi\) radians, we are at the point directly to the left of the origin on the unit circle.

So, \(\cos(\pi) = -1\).

### Determining the Correct Answer:

Given that \(\cos(\pi) = -1\) and the \(x\)-coordinate of point \(C\) is \(-1\), the correct answer is:

**(Escolha E) A coordenada de \(x\) do ponto \(C\)**.

Would you like any further explanation or have any other questions about this problem?

Here are 5 related questions that might interest you:

1. How do you calculate \(\sin(\pi)\) using the unit circle?
2. What is the significance of the unit circle in trigonometry?
3. How do we find the coordinates of any point on the unit circle for a given angle?
4. What is the relationship between radians and degrees in angle measurement?
5. How do the cosine and sine values change as we move around the unit circle?

**Tip:** Remember that on the unit circle, the \(x\)-coordinate represents \(\cos(\theta)\) and the \(y\)-coordinate represents \(\sin(\theta)\) for any angle \(\theta\).

Explore the cosine function \( \cos(\pi) \) and its application in trigonometry. Analyze points A, B, and C on the unit circle and determine which coordinates match \( \cos(\pi) \). Ideal for high school students studying trigonometry.

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