If θ = 4/π3, find the exact value of each expression below.

(a) cos2θ=

(b) 2cosθ=

(c) cosθ2=




Given \( \theta = \frac{4}{\pi^3} \), we are to find the exact values of the following expressions:

(a) \( \cos 2\theta \)
(b) \( 2\cos \theta \)
(c) \( \cos \theta^2 \)

First, let's clarify each expression:

1. \( \cos 2\theta \) refers to the cosine of twice the angle \(\theta\).
2. \( 2 \cos \theta \) refers to twice the cosine of the angle \(\theta\).
3. \( \cos \theta^2 \) refers to the cosine of the square of the angle \(\theta\).

Given that the angle \(\theta\) is provided in an unconventional form, it seems likely that these expressions are intended to be evaluated symbolically. Here’s how we proceed:

### (a) \( \cos 2\theta \)
Using the double-angle formula for cosine:
\[ \cos

Explore how to evaluate the expressions cos 2θ, 2cos θ, and cos θ^2 given θ = 4/π^3. Learn the application of the double-angle formula for cosine and related trigonometric concepts. Suitable for advanced high school students in Grades 11-12.

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