Expressed as a function of an acute angle, `cos310^(@)`=

Options

A. `-sin50^(@)`
B. `-sin40^(@)`
C. `-cos50^(@)`
D. `cos50^(@)`

Explanation

To express \( \cos 310^\circ \) as a function of an acute angle, we can follow these steps:

### Step 1: Identify the Quadrant
The angle \( 310^\circ \) is located in the fourth quadrant since it is between \( 270^\circ \) and \( 360^\circ \). In the fourth quadrant, the cosine function is positive.

**Hint:** Remember that angles between \( 270^\circ \) and \( 360^\circ \) are in the fourth quadrant.

### Step 2: Use the Reference Angle
To find the acute angle (reference angle) corresponding to \( 310^\circ \), we can subtract it from \( 360^\circ \):
\[ \text{Reference angle} = 360^\circ - 310^\circ = 50^\circ \]

**Hint:** The reference angle in the fourth quadrant can be found by subtracting the angle from \( 360^\circ \).

### Step 3: Express Cosine in Terms of the Acute Angle
Using the property of the cosine function in the fourth quadrant, we have:
\[ \cos 310^\circ = \cos(360^\circ - 50^\circ) = \cos 50^\circ \]

**Hint:** Recall that \( \cos(360^\circ - \theta) = \cos(\theta) \) for any angle \( \theta \).

### Conclusion
Thus, we can express \( \cos 310^\circ \) as:
\[ \cos 310^\circ = \cos 50^\circ \]

**Final Answer:** \( \cos 310^\circ = \cos 50^\circ \)