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Aim: What does SOHCAHTOA have to do with our study of right triangles?

A. 4. 3. AC. BC. 4. AC. 5. =. =. =. 4. CB. AB. 3. 5. 5. AB. C. B. 3. Aim: What does SOHCAHTOA have to do with our study of right triangles?. Do Now:. What are the following ratios?. Key terms: adjacent , opposite & hypotenuse. A. 5. 4. 4. AB. 5. C. B. 3.

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Aim: What does SOHCAHTOA have to do with our study of right triangles?

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  1. A 4 3 AC BC 4 AC 5 = = = 4 CB AB 3 5 5 AB C B 3 Aim: What does SOHCAHTOA have to do with our study of right triangles? Do Now: What are the following ratios? Key terms: adjacent, opposite & hypotenuse

  2. A 5 4 4 AB 5 C B 3 Trigonometry Basics - Sine In a right DABC with right angle BCA • The sine of angle B, written sine B, is defined as AC sin B = =

  3. sin  = Sine’s Reciprocal What is the reciprocal of sin? 1/sin  What is the reciprocal of 3? 1/3 cosecant the reciprocal of sin has a special name: csc  = ? = ex. using the calculator to find csc 53º: Method 1 find csc 53º: 53 ENTER x -1 sin ENTER Display: 1.252135658

  4. A 5 4 5 AC 4 C B 3 Trigonometry Basics - Cosecant In a right DABC with right angle BCA • The cosecant of angle B, written csc B, is defined as AB csc B = =

  5. A 5 4 3 AB 5 C B 3 Trigonometry Basics - Cosine In a right DABC with right angle  BCA • The cosine of angle B, written cos B, is defined as BC cos B = = the sine of an acute angle has the same value as the cosine of its complement. Recall:

  6. cos  = ENTER ÷  = ? 2nd cos -1 1 2 Display: 60 using the calculator to find sec  : Method 2 Find sec (-38º): 1 ÷ ENTER ( – ) cos 38 Display: 1.269018215 Cosine’s Reciprocal The reciprocal of cosine  is the secant: sec  = ? 2 ex.

  7. A 5 4 5 BC 3 C B 3 Trigonometry Basics - Secant In a right DABC with right angle  BCA • The secant of angle B, written sec B, is defined as AB sec B = =

  8. A 5 4 4 BC 3 C B 3 Trigonometry Basics - Tangent In a right DABC with right angle  BCA • The tangent of angle B, written tan B, is defined as AC tan B = =

  9. ENTER Display: 60  = ? 2nd tan -1 Using the calculator to find cot  : Find cot 257º: tan ENTER x -1 ENTER 257 Method 1 Display: .2308681911 ÷ ENTER tan 1 257 Method 2 Display: .2308681911 Tangent’s Reciprocal The reciprocal of tan  is the cotangent: = cot  = ? tan  = ex.

  10. A 5 4 3 AC 4 C B 3 Trigonometry Basics - Cotangent In a right DABC with right angle  BCA • The cotangent of angle B, written cot B, is defined as BC cot B = =

  11. Opposite Hypotenuse Sine - SOH = Adjacent Hypotenuse Cosine - CAH = Opposite Adjacent Tangent - TOA = Meet Chief SOH CAH TOA

  12. A 5 4 B C 3 Trig. Relationships Recall: the sine of an acute angle has the same value as the cosine of its complement. sin A = cos B and cos A = sin B the tangent of an acute angle has the same value as the cotangent of its complement. tan A = cot B and cot A = tan B The tangent of an acute angle is the reciprocal of the tangent of its complement tan A· tan B = 1

  13. Model Problem In right triangle ABC with right angle at C, BC = 6, and AC = 8. Find the three trigonometric functions of  B. A 10 8 B C 6 sin B = cos B = tan B =

  14. 3’ Model Problem Park planners would like to build a bridge across a creek. Surveyors have determined that from 5 ft. above the ground the angle of elevation to the top of an 8ft. pole on the opposite side of the creek is 5o. Find the length of the bridge to the nearest foot. 5o x 5’ 8’

  15. Model Problems • sin 24o is equivalent to • a) cos 24o b) sin 66o c) cos 660 d) 1/sin 240 The sine of an angle has the same value as the cosine of its complement. 2. If cot x = tan(x + 20o), find x. When the cotangent and tangent functions are equal in value, the angles must be complementary. x + (x + 20) = 90 2x + 20 = 90 x = 70

  16. Degrees, Minutes & Seconds 3600 in a circle 60 minutes in 1 degree 1 minute is 1/60th of a degree 60 seconds in 1 minute 1 second is 1/60th of a minute 17o 43’05” 17 degrees 43 minutes 5 seconds

  17. Model Problem Find cos 17o 43’ to 4 decimal places Find sin 20.30o to 4 decimal places Find sin 20o 30’ to 4 decimal places

  18. 2nd cos -1 2nd 3 ÷ 2 ENTER Find An Angle Given a Trig Function Value What is measure of ? Calculator’s MODE must be in degrees 30o What is measure of ?

  19. Regents Prep In triangle ABC, side a = 7, b = 6, and c= 8. Find m B to the nearest degree. • 1) 43o 2) 47o • 3) 65o 4) 137o

  20. Regents Prep In the diagram below of right triangle KTW, KW = 6, KT = 5, and mKTW = 90. • What is the measure of K, to the nearest minute? • 33o33’ 2) 33o55’ • 3) 33o34’ 4) 33o56’

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