How to Use a Sine Function
A right triangle has a 90-degree angle within the interior and three sides, two shorter sides offset by a longer, slanted side called the hypotenuse. The Pythagorean theorem defines the relationship of the sides as a^2 + b^2 = c^2, where "a" and "b" are the shorter sides and "c" is the hypotenuse. The trigonometric functions of sine, cosine and tangent are defined by the relationship of two of the sides compared to one of the non-90-degree internal angles.
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Instructions
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Solve a problem including the sine function using its definition of sin(degree) = opposite side / hypotenuse, where the "degree" is the number degree of the angle in question and "opposite side" is the side of the triangle across from that angle.
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Practice solving the sine function for a triangle with an angle of 45 degrees, an adjacent side of 4 and a hypotenuse of 6. Note that the adjacent side is given but the opposite side is needed.
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3
Find the opposite side using the Pythagorean theorem. Plug in the known information; 4^2 + b^2 = 6^2. Simplify: 16 + b^2 = 36. Subtract 16 from both sides: b^2 = 20. Take the square root of both sides to eliminate the exponent: b = √20.
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Write out the sine function formula with the known information plugged in: sin(45 degrees) = √20 / 6 = 0.745355992 or 0.75 (rounded).
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