For each of the following, find the value of $$ heta $$ for $$ 0 \leqslant heta \leqslant \pi $$. $$ \begin{array}{ll} ext { (a) } \cos heta=0.445 & ext { (b) } \cos \end{array} $$

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For each of the following, find the value of $$ 	heta $$ for $$ 0 \leqslant 	heta \leqslant \pi $$. $$ \begin{array}{ll}	ext { (a) } \cos 	heta=0.445 & 	ext { (b) } \cos \end{array} $$

UpStudy AI · Accepted Answer

To solve for $$ \theta $$ in the equation $$ \cos \theta = 0.445 $$ within the interval $$ 0 \leqslant \theta \leqslant \pi $$, we'll follow these steps:

### (a) $$ \cos \theta = 0.445 $$

#### Step 1: Use the Inverse Cosine Function
To find $$ \theta $$, we take the inverse cosine (also known as arccos) of both sides:
$$
\theta = \cos^{-1}(0.445)
$$

#### Step 2: Calculate the Angle
Using a calculator, ensure it's set to the desired unit (degrees or radians).

- **In Degrees:**
  $$
  \theta \approx \cos^{-1}(0.445) \approx 63.56^\circ
  $$

- **In Radians:**
  $$
  \theta \approx \cos^{-1}(0.445) \approx 1.106 \text{ radians}
  $$

#### Step 3: Consider the Interval $$ 0 \leqslant \theta \leqslant \pi $$
Since the cosine function is positive in both the first and fourth quadrants, but we're limited to $$ 0 \leqslant \theta \leqslant \pi $$ (which corresponds to the first and second quadrants), we only have one solution in this interval:
$$
\theta \approx 63.56^\circ \quad \text{or} \quad \theta \approx 1.106 \text{ radians}
$$

### Summary
$$
\boxed{\theta \approx 63.56^\circ \quad \text{or} \quad \theta \approx 1.106 \text{ radians}}
$$

*Note:* If you intended to provide part (b) of the problem, please ensure the complete equation is included so I can assist you further.
$$ \theta \approx 63.56^\circ $$ or $$ \theta \approx 1.106 $$ radians

For each of the following, find the value of \( \theta \) for \( 0 \leqslant \theta \leqslant \pi \). \( \begin{array}{ll}\text { (a) } \cos \theta=0.445 & \text { (b) } \cos \end{array} \)

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