**What has the same sine value as 90?**
When we look at the trigonometric functions, the sine of an angle is a fundamental concept. Sine is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse in a right triangle. The value of the sine function ranges from -1 to 1, with specific values for certain angles. One such angle is 90 degrees, also known as a right angle. So, what has the same sine value as 90?
**The answer to this question is 1.** Yes, the sine of 90 degrees is equal to 1. This means that the length of the side opposite the angle of 90 degrees is equal to the length of the hypotenuse in a right triangle.
Having understood what has the same sine value as 90, let’s explore some related or similar frequently asked questions about trigonometric functions:
1. What is the sine function?
The sine function is a mathematical function that relates the angles of a right triangle to the ratios of the triangle’s sides.
2. How is the sine function calculated?
To calculate the sine of an angle, divide the length of the side opposite the angle by the length of the hypotenuse in a right-angled triangle.
3. What is the range of the sine function?
The sine function has a range of -1 to 1, meaning its values can never be less than -1 or greater than 1.
4. Are there other angles with a sine value of 1?
Yes, there are other angles in which the sine value is equal to 1. One such angle is 270 degrees.
5. What is the relationship between the sine values of complementary angles?
The sine values of complementary angles are equal. For example, the sine of 30 degrees and the sine of 60 degrees are both equal to 0.5.
6. Can the sine function be negative?
Yes, the sine function can be negative for angles in the third and fourth quadrants of the unit circle.
7. What is the sine of 0 degrees?
The sine of 0 degrees is 0. It means there is no length of the side opposite the angle in a right triangle.
8. What is the sine of 180 degrees?
The sine of 180 degrees is 0. It indicates that the length of the side opposite the angle is equal to the length of the hypotenuse but in opposite directions.
9. How does the sine function relate to the unit circle?
In the unit circle, the y-coordinate of a point on the circle corresponds to the sine value of the angle formed with the positive x-axis.
10. What happens when the angle is greater than 90 degrees?
For angles greater than 90 degrees, the sine function becomes negative as the side opposite the angle becomes shorter than the hypotenuse.
11. Is there a relationship between sine and cosine?
Yes, there is. The sine and cosine functions are related through the Pythagorean identity: sin^2(theta) + cos^2(theta) = 1.
12. Are there applications of the sine function in real-life?
Yes, the sine function finds applications in various fields like physics, engineering, and architecture, as it can model many periodic phenomena such as waves and vibrations.
Understanding the concept of the sine function and its value at 90 degrees provides a strong foundation for trigonometry and its practical use in various industries. So, the next time someone asks you what has the same sine value as 90, you can confidently give them the answer: 1.