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

5. 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

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

7. 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

8. 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

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

10. Calculator  When using  trig functions, your calculator must be in Degree mode

11. 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