What is the value of sin(45°)? (2016)

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Question: What is the value of sin(45°)? (2016)

Options:

Correct Answer: 1/√2

Solution:

sin(45°) = 1/√2

What is the value of sin(45°)? (2016)

What is the value of sin(45°)? (2016)

Step 1: Understand that sin(45°) refers to the sine of a 45-degree angle.
Step 2: Recall that 45 degrees is a special angle in trigonometry.
Step 3: Remember that for a 45-degree angle in a right triangle, the opposite and adjacent sides are equal.
Step 4: Use the formula for sine, which is sin(angle) = opposite side / hypotenuse.
Step 5: For a 45-degree angle, if the sides are equal, we can say opposite = 1 and adjacent = 1.
Step 6: Calculate the hypotenuse using the Pythagorean theorem: hypotenuse = √(1² + 1²) = √2.
Step 7: Substitute the values into the sine formula: sin(45°) = opposite / hypotenuse = 1 / √2.
Step 8: Conclude that sin(45°) = 1/√2.

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