Pg. 324 Homework
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Transcript of Pg. 324 Homework
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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• #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°
9 17 7 15, , ,4 4 4 4
13 25 11 23, , ,6 6 6 6
5 11 7 13, , ,3 3 3 3
2,
6 3 3 8,
26 13
23180
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6.5 Trig Functions of an Acute Angle
Trig Functions• The six trig functions of any
angle 0° < Ɵ < 90° are defined as follows:
• Also, we know that from the basic three trig functions:
sin cot
cos sec
tan csc
opp adjhyp oppadj hyphyp adjopp hypadj opp
1cottan1seccos1cscsin
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6.5 Trig Functions of an Acute Angle
Triangle Trig• 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!!
• If c = 2, determine the lengths of a and b and find the six trig values at 30° and 60°.
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6.5 Trig Functions of an Acute Angle
More Trig Triangles• If a = 1, determine the
length of c and find the six trig values.
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:
sin cos cot tan2 2
cos sin sec csc2 2
tan cot csc sec2 2
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6.5 Trig Functions of an Acute Angle
Example:• Show that
are cofunctions. • 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.
sin cos2
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6.5 Trig Functions of an Acute Angle
Example:• They hypotenuse and one
leg of a triangle measure 8 and 5 respectively. Find the measure of angle Ɵ formed by these two sides.
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:sin cos tan
sec csc cot
y x yr r xr r xx y y
2 2x y
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6.5 Trig Functions of an Acute Angle
Example:• 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!!
• 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:
30, , , , 22 2