Chapter 13: Q49. (page 708)

If the secant of angle $(θ)$ is $\frac{25}{7}$ , what is sine of angle $(θ)$ .
role="math" localid="1648481459730" $(A) \frac{5}{25} (B) \frac{7}{25} (C) \frac{24}{25} (D) \frac{25}{7}$

Short Answer

Expert verified

The value of $\sin e (θ) = \frac{24}{25}$ . So, option (C) is correct.

Step by step solution

Step 1. Write down the given information.

It is given that $\sec (θ) = \frac{25}{7}$

Step 2. Calculation.

Since $\sec (θ) = \frac{25}{7}$ , so by reciprocal identity $\cos (θ) = \frac{7}{25}$ . Therefore, construct the triangle having angle $C = θ$ , base $B C = 7$ , hypotenuse $A C = 25$ and angle $B = 90 °$ .

Now, by Pythagoras Theorem,

$\begin{matrix} A C^{2} = A B^{2} + B C^{2} \\ 25^{2} = A B^{2} + 7^{2} \\ A B^{2} = 25^{2} - 7^{2} \\ A B = \sqrt{25^{2} - 7^{2}} \\ A B = 24 \end{matrix}$

Now in right triangle ABC by trigonometric ratios,

$\begin{matrix} \sin (C) = \frac{A B}{A C} \\ \sin (θ) = \frac{24}{25} \end{matrix}$

Since, the value of $\sin (θ) = \frac{24}{25}$ . Hence, option (C) is correct.

Step 3. Conclusion.

The value of $\sin (θ) = \frac{24}{25}$ . Hence, option (C) is correct.

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If the secant of angle $(θ)$ is $\frac{25}{7}$ , what is sine of angle $(θ)$ .
role="math" localid="1648481459730" $(A) \frac{5}{25} (B) \frac{7}{25} (C) \frac{24}{25} (D) \frac{25}{7}$

Short Answer

Step by step solution

Step 1. Write down the given information.

Step 2. Calculation.

Step 3. Conclusion.

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If the secant of angle θ is 257, what is sine of angle θ.role="math" localid="1648481459730" A525B725C2425D257

Short Answer

Step by step solution

Step 1. Write down the given information.

Step 2. Calculation.

Step 3. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Discrete Mathematics

Probability and Statistics

Statistics

Logic and Functions

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

If the secant of angle $(θ)$ is $\frac{25}{7}$ , what is sine of angle $(θ)$ .
role="math" localid="1648481459730" $(A) \frac{5}{25} (B) \frac{7}{25} (C) \frac{24}{25} (D) \frac{25}{7}$