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ext{Sin}
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Q. ext{Sin}
- Understand Sine Definition: Recognize that refers to the sine of a -degree angle.Sine is a trigonometric function that gives the ratio of the length of the opposite side to the length of the hypotenuse in a right-angled triangle.
- Recall Special Triangle: Recall the special triangle for a -degree angle, which is an isosceles right triangle. In such a triangle, the sides opposite the -degree angles are equal, and the hypotenuse is times longer than either of the other two sides.
- Apply Sine Definition: Use the definition of sine in a right triangle.For a -degree angle, the sine is the ratio of the length of the side opposite the angle to the length of the hypotenuse.Since the triangle is isosceles, the side opposite the -degree angle is the same length as the adjacent side.
- Calculate Sine of Degrees: Calculate the sine of degrees using the special triangle.The length of the side opposite the -degree angle is (if we assume the sides to be unit for simplicity), and the length of the hypotenuse is .So, .
- Rationalize Denominator: Rationalize the denominator to express the sine value in a more standard form.To rationalize the denominator, multiply the numerator and the denominator by .
