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Sine and arc sine

Sine and arc sine. A temporary mathematical detour. Sides of a Right Angle Triangles. A right angle triangle has 3 sides, and 2 sides are perpendicular to each other The longest side of a right angle triangle is called the hypotenuse. Hypotenuse. Sides of a right angle triangle.

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Sine and arc sine

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  1. Sine and arc sine A temporary mathematical detour

  2. Sides of a Right Angle Triangles • A right angle triangle has 3 sides, and 2 sides are perpendicular to each other • The longest side of a right angle triangle is called the hypotenuse. Hypotenuse

  3. Sides of a right angle triangle • Other than the hypotenuse, the other sides of a right angle triangle must be made in reference to an angle: • Consider the triangle below: y Hypotenuse Hypotenuse Opposite Adjacent x Adjacent Opposite

  4. sine • There are 3 trigonometric functions: sine, cosine and tangent. • In Physics, you will only need to use sine. (short form: sin) • The Sine of an angle is defined as length of opposite side divided by length of hypotenuse Opposite Hypotenuse x Adjacent

  5. sine • For example, consider triangle below • What is sin x? • Opposite side = 4 m • Hypotheneus = 5 m • Recall: Sin x = opposite / hypotheneus • = 4/5 • = 0.8 (no units!) 5 m 4 m • Note: • You can only Sine an angle • Trigo identities have no units • Sine and Cosine are always less than 1 x

  6. Arc sine • Arc Sine is the opposite of Sine (sometimes called “inverse sine”) • Symbol of Arc Sine is sin-1 • For Sine, I give you an angle, and you give me a ratio (i.e. length of opposite side divided by hypotheneus) • For Arc Sine, I give you the ratio, you give me the angle Sin x = 0.8 Sin -1 (0.8) = x (in degrees) [Can you find Sin-1 using your calculator?] Sin -1 (0.8) = 53.1° (1 decimal place) Note: this presentation is okay for Physics exam, but is not allowed for Math exam!! 5 m 4 m x

  7. Test yourself • Find Angle x using Arc Sine Sin x = 6/10 = 0.6 Sin -1 (0.6) = x [Use calculator] X = 36.9° (1 decimal place) 10 m 6 m x

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