Pg. 323/361 Homework• Pg. 362 #39 – 47 odd, 51, 52

Memorize Trig. Info

• #2 QIV #4 QIII #6 QIII• #8 -250°#10 470°• #12 338°, 698°, -382°, -742° #14 210°, 570°, -510°, -870°• #16 11π/4, -5π/2 #18 29π/6, -19π/6• #20 π/4, 9π/4, -15π/4, -23π/4 #22 67°, 157°• #24 78°, 168° #26 5π/12, 11π/12 #28 π/14, 4π/7• #30 90°, π/2 #32 135°, 3π/4 #34 0°, 0, 2π• #36 -120°, -2π/3 #38 -600°, -10π/3 #40 -1260°, -7π• #42 π/3 #44 7π/6 #46 11π/6• #48 59π/90 #50 249π/180 #52 810/π• #1 #2 #3 8/7• #4 7/8 #5 #6• #7• #8 11/15 #9 #10• #11 #12 #13 15/11

8113

7113

1137

1138

2 2615

152 26

2 2611

112 26

113 1137 8 7 8, , , , ,8 7 8 7113 113

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

6.5 Trig Functions of an Acute Angle

Example:• They hypotenuse and one

leg of a triangle measure 12 and 7 respectively. Find the measure of angle Ɵ formed by these two sides.

• Let Ɵ be an acute angle such that sin Ɵ = 5/6. Find all the trig functions of Ɵ.

• One angle of a right triangle measures 38°, and the hypotenuse has length of 17. Find the measures of the remaining sides.

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(4, 7) 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, 4) 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

6.5 Trig Functions of an Acute Angle

Determining Ɵ• Given the following, find the

measure of Ɵ in both degrees and radians.

1sin2

4cos5

tan 1

csc 2 sec 3

3cot5

csc 2

6.5 Trig Functions of an Acute Angle

Proving.• Can you prove that

6•5+2 = 7•5 – 3 • How do you know this?• Prove that:

• Prove that:2 2 2cos sin 2cos 1t t t

sin costanx xx