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Chapter 13: Q49. (page 708)

If the secant of angle $(胃)$ is $\frac{25}{7}$ , what is sine of angle $(胃)$ .
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 $\sin e (胃) = \frac{24}{25}$ . So, option (C) is correct.

Step by step solution

01

Step 1. Write down the given information.

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

02

Step 2. Calculation.

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

Now, by Pythagoras Theorem,

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

Now in right triangle ABC by trigonometric ratios,

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

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

03

Step 3. Conclusion.

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

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Most popular questions from this chapter

Rewrite each degree measure in radians and each radian measure in degrees if the angle is $570 掳$ .

Rewrite each degree measure in radians and each radian measure in degrees if the angle is $260 掳$ .

Draw an angle with given measure of $570 掳$ in standard position.

Name the set of numbers to which angle measures belong.

Find the area of regular hexagon with point $O$ as its center.

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