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Pg. 324 Homework

Pg. 324 Homework. Memorize familiar radian measure angles Pg. 323 #2 – 52 even Pg. 361 #1 – 13 all #1 QIII #3 QII #5 QI #7 408° #9 345° #11 415°, 775°, -305°, -665° #13 50°, 770°, -510°, -870° #15 #17 #19 #21 55°, 145° #23 22°, 112° #25 #27

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Pg. 324 Homework

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  1. Pg. 324 Homework • Memorize familiar radian measure anglesPg. 323 #2 – 52 even Pg. 361 #1 – 13 all • #1 QIII #3 QII #5 QI • #7 408° #9 345° • #11 415°, 775°, -305°, -665° #13 50°, 770°, -510°, -870° • #15 #17 • #19 #21 55°, 145° • #23 22°, 112° #25 #27 • #29 180° or π #31 45° or π/4 #33 315° or 7π/4 • #35 180° or π #37 480° or 8π/3 #39 900° or 5π • #41 π/4 #43 3π/4 #45 2π/3 • #47 #49 2π/5 #51 75° • #53 214.86°

  2. 6.5 Trig Functions of an Acute Angle Trig Functions Also, we know that from the basic three trig functions: • The six trig functions of any angle 0° < Ɵ < 90° are defined as follows:

  3. 6.5 Trig Functions of an Acute Angle Triangle Trig If c = 2, determine the lengths of a and b and find the six trig values at 30° and 60°. • We use right triangles because they allow us to use the Pythagorean Theorem, which makes solving a much easier process! • Because 30°, 45° and 60° occur frequently, we will learn and memorize those triangles!!

  4. 6.5 Trig Functions of an Acute Angle More Trig Triangles Cofunctions of Complementary Angles If Ɵ is any acute trig angle, a trig function value of Ɵ is equal to the cofunction of the complement of Ɵ, as follows: • If a = 1, determine the length of c and find the six trig values.

  5. 6.5 Trig Functions of an Acute Angle Example: Let Ɵ be an acute angle such that sin Ɵ = ¾. Find all the trig functions of Ɵ. One angle of a right triangle measures 42°, and the hypotenuse has length of 10. Find the measures of the remaining sides. • Show that are cofunctions.

  6. 6.5 Trig Functions of an Acute Angle Example: Trig Functions of Any Angle Let Ɵ be an angle in standard position, P(x, y) a point other than the origin on the terminal side of P, and r = The six trig values of Ɵ are defined as follows: • They hypotenuse and one leg of a triangle measure 8 and 5 respectively. Find the measure of angle Ɵ formed by these two sides.

  7. 6.5 Trig Functions of an Acute Angle Example: Find the values of all six trig functions and the angle of measure of angle Ɵ, where P(-3, 2) is a point on the terminal side of Ɵ. Find all the values of all six trig functions for the quadrantal angles of: • Find the values of the six trig functions at an angle Ɵ in standard form with point P(2, 4) on its terminal side. • **Note** If an angle does not appear acute in the first quadrant, you can work in any of the four quadrants to make the angle acute!!

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