Answer :
To find the value of [tex]\(\sin 74^\circ\)[/tex], we need to consider the sine function for this specific angle.
1. Understanding Sine in Degrees: The sine function helps us determine the ratio of the opposite side to the hypotenuse in a right-angled triangle for a given angle. Here, we are interested in [tex]\(\sin 74^\circ\)[/tex].
2. Conversion to Radians: In mathematics, trigonometric functions often use radians. The conversion from degrees to radians is essential when performing calculations using trigonometric functions since many calculators and mathematical software utilize radians by default.
3. Calculation Process:
- Convert the angle from degrees into radians:
[tex]\[
\text{Radians} = \frac{\pi}{180^\circ} \times \text{Degrees}
\][/tex]
So, [tex]\(74^\circ\)[/tex] in radians is approximately [tex]\(1.29\)[/tex].
4. Finding the Sine Value: Now that we have the angle in radians, we can find the sine value for this angle. The sine value of an angle tells us the ratio of the length of the opposite side to the hypotenuse of a right triangle.
5. Final Result: The sine of [tex]\(74^\circ\)[/tex] is approximately [tex]\(0.9612\)[/tex]. This means that, in a right-angled triangle with a [tex]\(74^\circ\)[/tex] angle, the length of the side opposite this angle is about 0.9612 times the hypotenuse.
Therefore, [tex]\(\sin 74^\circ \approx 0.9612\)[/tex].
1. Understanding Sine in Degrees: The sine function helps us determine the ratio of the opposite side to the hypotenuse in a right-angled triangle for a given angle. Here, we are interested in [tex]\(\sin 74^\circ\)[/tex].
2. Conversion to Radians: In mathematics, trigonometric functions often use radians. The conversion from degrees to radians is essential when performing calculations using trigonometric functions since many calculators and mathematical software utilize radians by default.
3. Calculation Process:
- Convert the angle from degrees into radians:
[tex]\[
\text{Radians} = \frac{\pi}{180^\circ} \times \text{Degrees}
\][/tex]
So, [tex]\(74^\circ\)[/tex] in radians is approximately [tex]\(1.29\)[/tex].
4. Finding the Sine Value: Now that we have the angle in radians, we can find the sine value for this angle. The sine value of an angle tells us the ratio of the length of the opposite side to the hypotenuse of a right triangle.
5. Final Result: The sine of [tex]\(74^\circ\)[/tex] is approximately [tex]\(0.9612\)[/tex]. This means that, in a right-angled triangle with a [tex]\(74^\circ\)[/tex] angle, the length of the side opposite this angle is about 0.9612 times the hypotenuse.
Therefore, [tex]\(\sin 74^\circ \approx 0.9612\)[/tex].
