Find the value of Trigonometric expression cos ( -1125° ).

To find the value of the trigonometric expression cos(-1125°), we can simplify the angle first. Since cosine is periodic with a period of 360°, we can add or subtract multiples of 360° to find an equivalent angle within the standard range of 0° to 360°.

Step 1: Simplifying the Angle

First, we can add 360° multiple times to -1125° until we get a positive angle:

• -1125° + 3 × 360° = -1125° + 1080° = -45°

Now, we can add another 360° to -45°:

• -45° + 360° = 315°

Step 2: Finding the Cosine Value

Now that we have simplified the angle to 315°, we can find the cosine value:

• cos(315°) = cos(360° - 45°) = cos(45°)

Since cosine is positive in the fourth quadrant:

• cos(45°) = √2/2

Final Result

Therefore, the value of cos(-1125°) is √2/2.