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Lesson 46

Lesson 46. Finding trigonometric functions and their reciprocals. This lesson introduces trigonometry , which is the study of right triangles. A trigonometric ratio is a ratio of the lengths of any 2 sides of a right triangle.

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Lesson 46

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  1. Lesson 46 Finding trigonometric functions and their reciprocals

  2. This lesson introduces trigonometry, which is the study of right triangles. • A trigonometric ratio is a ratio of the lengths of any 2 sides of a right triangle. • A function whose rule is a trigonometric ratio is a trigonometric function. • Three common trigonometric functions are sine, cosine and tangent- abbreviated sin, cos, tan

  3. Trigonometric functions • The sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse sinA =opp • hyp • The cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse cosA= adj • hyp • The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side tanA= opp • adj

  4. Finding the values of sine, cosine and tangent • Find sin, cos and tan of angle A A hyp 40 adj 24 C 32 B opp

  5. Find sin, cos, and tan of angle B B 24 25 A 7 C

  6. Cosecant, secant and cotangent- • Abbreviations: csc, sec, and cot • These are the reciprocals of sin, cos, and tan • Cosecant is reciprocal of sin csc = 1 = hyp • sin opp • Secant is reciprocal of cos sec = 1 = hyp • cos adj • Cotangent is reciprocal of tan cot = 1 = adj • tan opp

  7. Finding values of csc, sec, and cot • Identify the hypotenuse, identify the side opposite angle B, identify the side adjacent to angle B. • Find the csc, sec and cot of angle B 24 C 10 B 26 A

  8. Find csc, sec, cot of angle B C 20 B 15 25 A

  9. Calculator • When using • trig functions, your calculator must be in Degree mode

  10. Finding the side of a triangle • Identify the known lengths , so you can decide which function to use. • In this example you use the sin because in relation to the 420 angle you have the opposite and the hypotenuse. • Sin 42 = opp = x • hyp 32 • 32( sin 42)= x • X= 21.4 42 32 x

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