Understanding the Sine Function | Finding the Value of sin(135°)

sin(135°)

To find the value of sin(135°), we need to understand that sin(x) represents the sine function

To find the value of sin(135°), we need to understand that sin(x) represents the sine function. In trigonometry, the sine function relates the ratio of the length of one side of a right triangle (opposite) to the length of the hypotenuse.

In this case, to find the value of sin(135°), we draw a right triangle with an angle of 135°. Since we’re dealing with a 135° angle, which is greater than 90°, the triangle will be in the second quadrant.

Now, let’s construct a right triangle with an angle of 135°. The reference angle in the first quadrant that has the same sine as 135° is 45°. We can then create a special right triangle – an isosceles right triangle with equal sides of length 1 unit.

By analyzing this triangle, we can see that the length of the opposite side is 1, and the length of the hypotenuse is √2. Remember, the hypotenuse is always the longest side of a right triangle.

From the definition of the sine function, sin(x) = opposite/hypotenuse, we can apply this to our triangle:

sin(135°) = 1/√2

To rationalize the denominator, we multiply the numerator and denominator by √2:

sin(135°) = (1/√2) * (√2/√2)

This simplifies to:

sin(135°) = √2/2

Therefore, the value of sin(135°) is √2/2.

More Answers:
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How to Calculate sin(120°) | Understanding the Sine Function and Using the Unit Circle

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