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Trigonometric Functions 2.2 – Definition 2

Trigonometric Functions 2.2 – Definition 2. JMerrill, 2006 Revised, 2009 (contributions from DDillon). Angle of Elevation Review.

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Trigonometric Functions 2.2 – Definition 2

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  1. Trigonometric Functions2.2 – Definition 2 JMerrill, 2006 Revised, 2009 (contributions from DDillon)

  2. Angle of Elevation Review • The angle of elevation of from the ground to the top of a mountain is 68o. If a skier at the top of the mountain is at an elevation of 4,200 feet, how long is the ski run from the top to the base of the mountain? • 4,529.85 feet

  3. Navigation Review • If a plane takes off on a heading of N 33o W and flies 12 miles, then makes a right (90o) turn, and flies 9 more miles, what bearing will the air traffic controller use to locate the plane? How far is the plane from where it started? • The plan is 15 miles away on a bearing of N 8.41o E

  4. Defining Trig Functions Let there be a point P (x, y) on a coordinate plane. P(x, y) y r r is the distance from the origin to the point P, which can be represented as being on the terminal side of θ. Since r represents a distance, it is always positive and cannot = 0. The six trigonometric functions are: θ x

  5. Definition 2 Remember, the denominator cannot ever = 0!

  6. Calculating Trig Values for Acute Angles If the terminal side of θ in standard position passes through point P (6, 8), draw θ and find the exact value of the six trig functions of θ. P(6, 8) r = 10 8 r is the hypotenuse and can be found using Pythagorean Thm: x2 + y2 = r2 θ 6

  7. You Do • If the terminal side of θ in standard position passes through point P (3, 7), draw θ and find the exact value of the six trig functions of θ.

  8. Calculating Trig Values for Nonacute Angles If the terminal side of θ in standard position passes through point P (-4, 2), draw θ and find the exact value of the six trig functions of θ. P(-4, 2) r = 2√5 2 θ -4

  9. Calculating Trig Values for Quadrant Angles • Find the exact value of the six trig functions when θ=90o • A convenient point on the terminal side of 90ois (0,1). So x = 0, y = 1, r = 1 (0,1) Now, if the angle is 180o, what point will you use?

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