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Lesson 46 Finding trigonometric functions and their reciprocals
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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
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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
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Finding the values of sine, cosine and tangent Find sin, cos and tan of angle A A B C 40 24 32 opp adj hyp
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Find sin, cos, and tan of angle B B A C 24 25 7
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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
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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 A C B 10 24 26
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Find csc, sec, cot of angle B A B C 15 25 20
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Calculator When using trig functions, your calculator must be in Degree mode
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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 42 0 angle you have the opposite and the hypotenuse. Sin 42 = opp = x hyp 32 32( sin 42)= x X= 21.4 x 42 32
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