C R A MA E N SI A

C R A MA E N SI A T E DRY N A A M P O R L A E IN A T I C S T H E M D E T O U R

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

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

SINE • For example, consider triangle below • What is sin x? 4 m • • • 5 m x • • Opposite side = 4 m Hypotheneus = 5 m Recall: Sin x = opposite / hypotheneus = 4/5 = 0. 8 (no units!) Note: You can only Sine an angle Trigo identities have no units Sine and Cosine are always less than 1

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 4 m 5 m x 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!!

TEST YOURSELF • Find Angle x using Arc Sine 6 m 10 m x Sin x = 6/10 = 0. 6 Sin -1 (0. 6) = x [Use calculator] X = 36. 9° (1 decimal place)