2.  Angles and Degree Measure › An angle is formed by two rays with a common endpoint › That endpoint is called the vertex › Angles can be labeled by the angle symbol (  ) and the vertex. The angle below may be labeled  A A angle side vertex

3.  Angles › Measured in degrees  1 degree (°) is 1/360 of a circle  180° is ½ a circle  90° (a right angle) is ¼ a circle  Minutes and seconds › A minute (‘) is 1/60 of a degree › A second (“) is 1/60 of a minute  Hence, 1 second = 1/3600 of a degree  Hint: It may be easier to convert between degree and DMS (Degree – Minute – Second) forms if you think of degrees as hours

4.  Converting between decimal form and DMS form  Write 35° 15’ 27” in decimal form › Divide minutes by 60 › Divide seconds by 3600 › Add all numbers together ›

5.  Converting between decimal form and DMS form (part 2)  Write 48.3625° in DMS form › The whole number is the degree. › Multiply by 60. The whole number is the minute. › Multiply by 60. The whole number is the second ›

6.  Similar Triangles and Trigonometric Ratios › Pneumonic Phrase: SOH-CAH-TOA › Learn it, live it, love it  sin (sine) = opposite / hypotenuse  cos (cosine) = adjacent / hypotenuse  tan (tangent) = opposite / adjacent › Reciprocals of trigonometric ratios  csc (cosecant) = 1 / sin = hypotenuse / opposite  sec (secant) = 1 / cos = hypotenuse / adjacent  cot (cotangent) = 1 / tan = adjacent / opposite › Remembering the reciprocal ratios  Tan/Cot as inverses is pretty self explanatory  Sin is inverse of CSC (S inverse of C)  Cos is inverse of SEC (C is inverse of S)

7.  Evaluating Trigonometric Ratios › Evaluate the six trigonometric ratios of the angle θ shown below ›  sin θ = 5 / 13csc θ = 13 / 5  cos θ = 12 / 13sec θ = 13 / 12  tan θ = 5 / 12cot θ = 12 / 5 θ 13 12 5

8.  Evaluating Trigonometric Ratios › Evaluate the six trigonometric ratios of 62° by using the triangle shown below ›  sin 62° = 3 / 3.4csc 62° = 3.4 / 3  cos 62° = 1.6 / 3.4sec 62° = 3.4 / 1.6  tan 62° = 3 / 1.6cot 62° = 1.6 / 3 θ 3 3.4 62° 1.6

9.  Evaluating Trigonometric Ratios on a calculator › Calculators have buttons to evaluate sin, cos, tan › To get the trigonometric ratio, simply input the angle value into your calculator.  Make sure you are in degree mode  2 nd → M ORE → 3 rd item down (we’ll be using radians later) › Evaluate the six trigonometric ratios of 20°  sin 20° ≈ 0.3420csc 20° = 1 / sin 20° ≈ 2.9238  cos 20° ≈ 0.9397sec 20° = 1 / cos 20° ≈ 1.0642  tan 20° ≈ 0.3640cot 20° = 1 / tan 20° ≈ 2.7475

10.  Special Angles › For 30-60-90 and 45-45-90 triangles, we use exact values instead of calculator estimates. › 30° 2 1 60° 45° 1 1

11.  Assignment › Page 419  Problems 1 – 31, odd problems  Copy the chart at the top of page 419  Begin to memorize the terms from that chart which are highlighted in blue  Hint: Start to memorize the fact that