The Trigonometric Functions and Right Triangles A P o w e r P o I n t L e s s o n By Michael V. Schuster Mathematics Faculty Our Lady of the Sacred Heart High School Coraopolis, Pennsylvania

Right Triangle Anatomy Hypotenuse Opposite  Adjacent

Right Triangle Anatomy  Hypotenuse Adjacent Opposite

 Trigonometric Functions as Ratios of Sides OPP SIN q HYP ADJ COS q = HYP ADJ COS q = HYP HYP OPP OPP TAN q = ADJ  ADJ

 Reciprocal Functions as Ratios of Sides HYP OPP SIN q CSC q OPP HYP = OPP HYP ADJ HYP COS q SEC q = ADJ HYP HYP OPP ADJ OPP COT q TAN q = ADJ OPP  ADJ

 3 5 4 5 5 3 3 4 4 Trigonometric Functions as Ratios of Sides ex: SIN q = 5 4 COS q = 5 5 3 3 TAN q = 4  4 A

Reference Triangles: 45o 1

Reference Triangles: 30o 60o 1 2

Trigonometric Identities ex: Let Find Reciprocal Functions Quotient Identities: Pythagorean Identities:

“Co-functions of complementary angles are equal” (*complementary = angles adding to 900) Thanks! So do you! Luv those shoes on you!… Wow you look great! 1 2 Cofunctions: “Co-functions of complementary angles are equal”

Inverse Trig Functions Basic Idea: Given the value of a trig function - find the angle that produces that value… ex: 1 2 Notation: Say: “The inverse sine of 1/2 = /6” ex: Calculator: Find  if cos = 0.8 B

Solving for Sides 10 530 y ex: opp hyp z opp adj 25 420

River  200 400

 40ft 30ft

For degree and minute symbol DMS Format Stands for Degrees / Minutes / Seconds Notation: o / // 1’ = 1/60th of a degree 1’’ = 1/60th of a minute (1/3600th of a o) ex: Convert 152o 15’ 29” into decimal degrees = 152.258 o Calculator: 2nd APPS For degree and minute symbol

ex: Convert 152.258 into DMS format… ALPHA + For seconds symbol ENTER For answer… o ex: Convert 152.258 into DMS format…

Evaluating Trig Functions on the Calculator Set mode to match units of problem OR leave calculator in radian mode and use degree symbol for degree problems. 2. csc / sec / cot = [1/sin] [1/cos] [1/tan] ex: sin -76.4o cot 1.5 sec 5o40’12”

HONORS HW 6.1 - 6.2 pg 419 #’s 1, 2, 5, 6, 10-13 all, 15, 16, 19-22 all, 25-29 all. pg 429 1-3 all, 7-10 all, 13, 14, 17, 18, 20, 21, 26, 27, 37-39 all, 42, 44, 45, 47, 48.