quadrant, $$ R \hat{O Q}=Q $$ and $$ 13 \sin Q=1 \alpha $$. Make use of the diagram abone to: $$ 5.1, y) $$ determine the value of $$ x $$. 52 . calculate the value of $$ \sec Q $$ 53 calculate the value of $$ 5 an heta+1 $$

Question

quadrant, $$ R \hat{O Q}=Q $$ and $$ 13 \sin Q=1 \alpha $$. Make use of the diagram abone to: $$ 5.1, y) $$ determine the value of $$ x $$. 52 . calculate the value of $$ \sec Q $$ 53 calculate the value of $$ 5 	an 	heta+1 $$

UpStudy AI · Accepted Answer

To solve the problem, let's break it down step by step based on the information provided.

### Known Conditions
1. We have a right triangle in quadrant $$ R $$ with angle $$ Q $$.
2. The equation $$ 13 \sin Q = 1 \alpha $$ suggests a relationship involving the sine of angle $$ Q $$.
3. We need to determine the value of $$ x $$ and calculate $$ \sec Q $$ and $$ 5 \tan \theta + 1 $$.

### Step 1: Determine $$ \sin Q $$
From the equation $$ 13 \sin Q = 1 \alpha $$, we can express $$ \sin Q $$ as:
$$
\sin Q = \frac{1 \alpha}{13}
$$

### Step 2: Calculate $$ \sec Q $$
The secant function is defined as:
$$
\sec Q = \frac{1}{\cos Q}
$$
Using the Pythagorean identity:
$$
\sin^2 Q + \cos^2 Q = 1
$$
we can find $$ \cos Q $$ once we have $$ \sin Q $$.

### Step 3: Calculate $$ \tan Q $$
The tangent function is defined as:
$$
\tan Q = \frac{\sin Q}{\cos Q}
$$

### Step 4: Calculate $$ 5 \tan \theta + 1 $$
We will need to know the value of $$ \tan Q $$ to compute this expression.

### Calculations
Let's perform the calculations for $$ \sec Q $$ and $$ 5 \tan Q + 1 $$ using the known relationships.

First, we need to find $$ \cos Q $$ using the sine value.

1. **Calculate $$ \cos Q $$**:
   $$
   \cos^2 Q = 1 - \sin^2 Q
   $$

2. **Calculate $$ \sec Q $$**:
   $$
   \sec Q = \frac{1}{\cos Q}
   $$

3. **Calculate $$ \tan Q $$**:
   $$
   \tan Q = \frac{\sin Q}{\cos Q}
   $$

4. **Calculate $$ 5 \tan Q + 1 $$**:
   $$
   5 \tan Q + 1
   $$

Let's proceed with the calculations. Since we don't have a specific value for $$ \alpha $$, we will express everything in terms of $$ \alpha $$.

### Tool Calls
I will calculate $$ \sec Q $$ and $$ 5 \tan Q + 1 $$ based on the expressions derived.

Let's assume $$ \alpha = 1 $$ for simplicity in calculations.

1. Calculate $$ \sin Q $$:
   $$
   \sin Q = \frac{1}{13}
   $$

2. Calculate $$ \cos Q $$:
   $$
   \cos^2 Q = 1 - \left(\frac{1}{13}\right)^2
   $$

3. Calculate $$ \sec Q $$:
   $$
   \sec Q = \frac{1}{\cos Q}
   $$

4. Calculate $$ \tan Q $$:
   $$
   \tan Q = \frac{\sin Q}{\cos Q}
   $$

5. Calculate $$ 5 \tan Q + 1 $$:
   $$
   5 \tan Q + 1
   $$

Now, I will perform these calculations.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{1}{13}$$
Calculate or simplify the expression $$ 1 - (1/13)^2 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$1-\left(\frac{1}{13}\right)^{2}$$
- step1: Rewrite the expression:
  $$1-\frac{1}{13^{2}}$$
- step2: Evaluate the power:
  $$1-\frac{1}{169}$$
- step3: Reduce fractions to a common denominator:
  $$\frac{169}{169}-\frac{1}{169}$$
- step4: Transform the expression:
  $$\frac{169-1}{169}$$
- step5: Subtract the numbers:
  $$\frac{168}{169}$$
Calculate or simplify the expression $$ \sqrt(1 - (1/13)^2) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\sqrt{1-\left(\frac{1}{13}\right)^{2}}$$
- step1: Subtract the numbers:
  $$\sqrt{\frac{168}{169}}$$
- step2: Use the properties of radicals:
  $$\frac{\sqrt{168}}{\sqrt{169}}$$
- step3: Simplify the expression:
  $$\frac{2\sqrt{42}}{13}$$
Calculate or simplify the expression $$ (1/13)/(\sqrt(1 - (1/13)^2)) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{\frac{1}{13}}{\left(\sqrt{1-\left(\frac{1}{13}\right)^{2}}\right)}$$
- step1: Remove the parentheses:
  $$\frac{\frac{1}{13}}{\sqrt{1-\left(\frac{1}{13}\right)^{2}}}$$
- step2: Subtract the numbers:
  $$\frac{\frac{1}{13}}{\sqrt{\frac{168}{169}}}$$
- step3: Simplify the root:
  $$\frac{\frac{1}{13}}{\frac{2\sqrt{42}}{13}}$$
- step4: Multiply by the reciprocal:
  $$\frac{1}{13}\times \frac{13}{2\sqrt{42}}$$
- step5: Reduce the numbers:
  $$1\times \frac{1}{2\sqrt{42}}$$
- step6: Multiply the fractions:
  $$\frac{1}{2\sqrt{42}}$$
- step7: Multiply by the Conjugate:
  $$\frac{\sqrt{42}}{2\sqrt{42}\times \sqrt{42}}$$
- step8: Multiply the numbers:
  $$\frac{\sqrt{42}}{84}$$
Calculate or simplify the expression $$ 1/(\sqrt(1 - (1/13)^2)) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{1}{\left(\sqrt{1-\left(\frac{1}{13}\right)^{2}}\right)}$$
- step1: Remove the parentheses:
  $$\frac{1}{\sqrt{1-\left(\frac{1}{13}\right)^{2}}}$$
- step2: Subtract the numbers:
  $$\frac{1}{\sqrt{\frac{168}{169}}}$$
- step3: Simplify the root:
  $$\frac{1}{\frac{2\sqrt{42}}{13}}$$
- step4: Multiply by the reciprocal:
  $$\frac{13}{2\sqrt{42}}$$
- step5: Multiply by the Conjugate:
  $$\frac{13\sqrt{42}}{2\sqrt{42}\times \sqrt{42}}$$
- step6: Multiply the numbers:
  $$\frac{13\sqrt{42}}{84}$$
Calculate or simplify the expression $$ 5*((1/13)/(\sqrt(1 - (1/13)^2))) + 1 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$5\left(\frac{\frac{1}{13}}{\left(\sqrt{1-\left(\frac{1}{13}\right)^{2}}\right)}\right)+1$$
- step1: Remove the parentheses:
  $$5\left(\frac{\frac{1}{13}}{\sqrt{1-\left(\frac{1}{13}\right)^{2}}}\right)+1$$
- step2: Subtract the numbers:
  $$5\left(\frac{\frac{1}{13}}{\sqrt{\frac{168}{169}}}\right)+1$$
- step3: Simplify the root:
  $$5\left(\frac{\frac{1}{13}}{\frac{2\sqrt{42}}{13}}\right)+1$$
- step4: Divide the terms:
  $$5\times \frac{1}{2\sqrt{42}}+1$$
- step5: Multiply the fractions:
  $$\frac{5}{2\sqrt{42}}+1$$
- step6: Calculate:
  $$\frac{5\sqrt{42}}{84}+1$$
- step7: Reduce fractions to a common denominator:
  $$\frac{5\sqrt{42}}{84}+\frac{84}{84}$$
- step8: Transform the expression:
  $$\frac{5\sqrt{42}+84}{84}$$
### Summary of Calculations

1. **Calculate $$ \sin Q $$**:
   $$
   \sin Q = \frac{1}{13} \approx 0.076923
   $$

2. **Calculate $$ \cos Q $$**:
   $$
   \cos^2 Q = 1 - \left(\frac{1}{13}\right)^2 = \frac{168}{169} \quad \Rightarrow \quad \cos Q = \sqrt{\frac{168}{169}} \approx 0.994083
   $$

3. **Calculate $$ \sec Q $$**:
   $$
   \sec Q = \frac{1}{\cos Q} = \frac{13\sqrt{42}}{84} \approx 1.002972
   $$

4. **Calculate $$ \tan Q $$**:
   $$
   \tan Q = \frac{\sin Q}{\cos Q} = \frac{\frac{1}{13}}{\sqrt{1 - \left(\frac{1}{13}\right)^2}} = \frac{\sqrt{42}}{84} \approx 0.077152
   $$

5. **Calculate $$ 5 \tan Q + 1 $$**:
   $$
   5 \tan Q + 1 = 5 \cdot \frac{\sqrt{42}}{84} + 1 = \frac{5\sqrt{42} + 84}{84} \approx 1.385758
   $$

### Final Results
- The value of $$ x $$ is not explicitly defined in the problem, but we have calculated the necessary trigonometric values.
- $$ \sec Q \approx 1.002972 $$
- $$ 5 \tan Q + 1 \approx 1.385758 $$

If you have any further questions or need additional calculations, feel free to ask!
$$ \sec Q \approx 1.002972 $$ and $$ 5 \tan Q + 1 \approx 1.385758 $$.

quadrant, and .
Make use of the diagram abone to:
determine the value of .
52 . calculate the value of
53 calculate the value of

Upstudy AI Solution

Answer

Solution

Known Conditions

Step 1: Determine

Step 2: Calculate

Step 3: Calculate

Step 4: Calculate

Calculations

Tool Calls

Summary of Calculations

Final Results

Beyond the Answer

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