Chapter 13: Q7. (page 706)

Write an equation involving $\sin, \cos or \tan$ that can be used to findx. Then solve the equation. Round measures of side to the nearest tenth and angles to the nearest degrees.

Short Answer

Expert verified

The equation is $cos23 {}^{\circ}= \frac{32}{x}$ .And the simplified value of $x = 34.8$ .

Step by step solution

Step 1. Write down the given information.

The given figure is shown below.

Step 2. Concept used.

The six trigonometric functions are $\sin θ, \csc θ, \cos θ, \sec θ, \tan θ, \cot θ$ .

Let $(x, y)$ be a point in X-Y plane and (r)be the length of a line segment drawn from the origin to the point.

In, $Δ O A B, O A = r, O B = x, A B = y$

Therefore, six trigonometric functions are;

$\begin{matrix} \sin θ = \frac{A B}{O A} = \frac{y}{r}, \csc θ = \frac{1}{\sin θ} = \frac{O A}{A B} = \frac{r}{y} \\ \cos θ = \frac{O B}{O A} = \frac{x}{r}, \sec θ = \frac{1}{\cos θ} = \frac{O A}{O B} = \frac{r}{x} \\ \tan θ = \frac{A B}{O B} = \frac{y}{x}, \cot θ = \frac{1}{\tan θ} = \frac{O B}{A B} = \frac{x}{y} \end{matrix}$

Step 3. Calculation.

The equation that can be used to find $(x)$ is written below.

$cos23 {}^{\circ}= \frac{32}{x}$

Now, the equation $cos23 {}^{\circ}= \frac{32}{x}$ is solved as,

$\begin{matrix} cos23 ° = \frac{32}{x} \\ x = \frac{32}{\cos 23 °} \\ x = 32 \sec (23 °) \\ x = 34.8 \end{matrix}$

Step 4. Conclusion.

The equation is $cos23 {}^{\circ}= \frac{32}{x}$ . And the simplified value of $x = 34.8$ .

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Write an equation involving $\sin, \cos or \tan$ that can be used to findx. Then solve the equation. Round measures of side to the nearest tenth and angles to the nearest degrees.

Short Answer

Step by step solution

Step 1. Write down the given information.

Step 2. Concept used.

Step 3. Calculation.

Step 4. Conclusion.

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Write an equation involving sin,cosortanthat can be used to findx. Then solve the equation. Round measures of side to the nearest tenth and angles to the nearest degrees.

Short Answer

Step by step solution

Step 1. Write down the given information.

Step 2. Concept used.

Step 3. Calculation.

Step 4. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Applied Mathematics

Calculus

Decision Maths

Discrete Mathematics

Statistics

Study anywhere. Anytime. Across all devices.

Write an equation involving $\sin, \cos or \tan$ that can be used to findx. Then solve the equation. Round measures of side to the nearest tenth and angles to the nearest degrees.