Find the value of z.
cos(
–
1066°)=
z
6
Write your answer as an integer or as a decimal rounded to the nearest hundredth

We are tasked with finding the value of \( \cos(-1066^\circ) = z \).

### Step 1: Simplify the angle
The cosine function is periodic with a period of \(360^\circ\), so we can simplify the angle by finding an equivalent angle between \(0^\circ\) and \(360^\circ\).

\[
-1066^\circ + 360^\circ \times 3 = -1066^\circ + 1080^\circ = 14^\circ
\]

Thus, \( \cos(-1066^\circ) = \cos(14^\circ) \).

### Step 2: Find the cosine of \(14^\circ\)
Using a calculator or a trigonometric table, we find:

\[
\cos(14^\circ) \approx 0.9703
\]

Thus, \( z = 0.9703 \).

### Final Answer:
The value of \( z \) is approximately \( 0.97 \) when rounded to the nearest hundredth.

---

Would you like further details on trigonometric simplifications or any other aspects? Here are some related questions to consider:

1. How can we find equivalent angles for other large or negative angles?
2. Why is the cosine function periodic, and what does this imply?
3. What other functions share the same periodicity as cosine?
4. How can we convert degrees into radians, and why is it useful?
5. How do sine and cosine relate to the unit circle?

**Tip:** Always reduce large or negative angles to their simplest form using the periodicity of trigonometric functions!

Find the value of z. cos(-1066°) = z. Write your answer as an integer or as a decimal rounded to the nearest hundredth.

Learn how to calculate the cosine of a large negative angle, cos(-1066°), using trigonometric periodicity. This problem covers key trigonometric concepts such as angle simplification and the periodic nature of cosine, with a solution rounded to the nearest hundredth. Suitable for students in Grades 9-12.

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