Understanding the Sin of an Angle: θ and 90°

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In summary, the sin of an angle θ is represented by the ratio of the opposite side to the hypotenuse, sinθ=p/h. When the angle θ is 90 degrees, the opposite side and the hypotenuse are equal, hence sin90=1 and p=h. However, this may seem confusing as the hypotenuse is typically the longest side of a right triangle. To better understand this concept, it is helpful to visualize the triangle and see how the sides relate to each other.
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anigeo
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sin of an angle θ is sinθ=p/h. again sin90=1 which means that p=h.but the hypotenuse is the longest side of a right triangle so how can it be equal to the perpendicular?
 
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anigeo said:
sin of an angle θ is sinθ=p/h. again sin90=1 which means that p=h.but the hypotenuse is the longest side of a right triangle so how can it be equal to the perpendicular?

Step back from the math for a moment and visualize this triangle.

You've got right triangle whose theta is 90 degrees. What does this triangle look like?

Does it make sense that, if its theta is 90, you'd have one side as long as the hypotenuse? Can you intuit how long the other side would be?
 
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Related to Understanding the Sin of an Angle: θ and 90°

1. What is the sin of an angle?

The sin of an angle is a mathematical concept that represents the ratio of the length of the side opposite the angle to the length of the hypotenuse in a right triangle. It is denoted by the symbol "sin" and is one of the six basic trigonometric functions.

2. How is the sin of an angle calculated?

The sin of an angle can be calculated using a scientific calculator or by using the Pythagorean theorem in a right triangle. The formula for calculating sin is sin(θ) = opposite/hypotenuse, where θ is the angle in question.

3. What is the significance of θ in understanding the sin of an angle?

θ is the symbol commonly used to represent an angle in mathematics. In the context of understanding the sin of an angle, θ represents the angle whose sin is being calculated.

4. Why is 90° significant in understanding the sin of an angle?

90° is significant because it represents a right angle in a right triangle. The sin of 90° is equal to 1, which means that the length of the side opposite the angle is equal to the length of the hypotenuse.

5. How is understanding the sin of an angle useful in science?

The sin of an angle is used in various scientific fields such as physics, engineering, and astronomy to calculate and analyze different types of waves, forces, and trajectories. It is also used in navigation and mapmaking to determine distances and angles between two points.

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