# 20 Days. Three days  One radian is the measure of the central angle of a circle subtended by an arc of equal length to the radius of the circle.

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20 Days

Three days

 One radian is the measure of the central angle of a circle subtended by an arc of equal length to the radius of the circle.

A circle with radius of 1 Equation x 2 + y 2 = 1

 Read 5.1 and Complete "What do you know about Trig" WS

 Angle – Set of points determined by two rays. Example { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://images.slideplayer.com/14/4213405/slides/slide_10.jpg", "name": " Angle – Set of points determined by two rays.", "description": "Example

 Coterminal angles - two angles with the same initial and terminal sides.  Straight angle – an angle whose sides line on a straight line and extend in opposite directions from the vertex.  Degrees – One unit of measuring an angle. One complete revolution in the counter clockwise direction is 360*.

 Using the x-y plane, the standard position of an angle has its vertex at the origin and its initial side as the positive x-axis.  If the terminal angle is rotated counter clockwise, the angle is positive.  If the terminal angle is rotated clockwise, the angle is negative.

 You should be familiar with the following terms:

 p359 (#1,3,9 - 11,13,15,16,29, 31a, 33a)  Read p349 - 351, 353(note blue box and below), 354 and example 5

 When more precise measurements are required, we can extend our measurement to more decimal places, or we can divide the degree into equal parts called minutes (denoted ‘) and seconds (denoted “).

 p359 (#4,6,12,14,21,24,25,28,30,32,35-37,39)

Four Days

 We can refer to the three sides of any right triangle in relation to a specific acute angle as the adjacent, opposite, and hypotenuse sides.

 The six trig functions are the sine, cosine, tangent, cosecant, secant, and cotangent.

cos tan

 Find the six trig values for θ in the triangle below.

 Find the six trig values for θ if θ is in standard position and P(2,-5) is on the terminal side.

 Find the values of x and y in the triangle below using trig functions.

 You are visiting Sequoia National Park in California to see the Giant Redwood Trees. You are standing 500ft away from the biggest tree that you can find and the angle between the ground and the top of the tree is 33 *. How tall is the tree?

 p375 (#2,3,9, 11, 21,22,24,27—exact answers until #21)  Read p362 - 365

 Find the six trig values for θ if θ is in standard position and is on the line y=-4x.

 Given that find the remaining trig values.

cos tan

 Recall that the unit circle has its center at (0,0) and a radius of 1. If we divide the special right triangles so the hypotenuse equals 1 we get that the points on the unit circle have coordinates.

 The the coordinates on the unit circle are of the form. We get the following values for 0, 30, 45, 60, and 90 degrees.

 You must memorize the following ASAP!!

 p375 (#4,12 ̶ 18 even, 28, 67,70,74,78)

 We can see that the 6 trig functions are reciprocals of one another. Sin and Csc are reciprocals, Cos and Sec are reciprocals, and Tan and Cot are also reciprocals.

All of the identities we learned are found in the back page of your book under the heading Trigonometric Identities and then Fundamental Identities. You'll need to have these memorized or be able to derive them for this course. RECIPROCAL IDENTITIES QUOTIENT IDENTITIES PYTHAGOREAN IDENTITIES

 We can verify that the following identity is true by making the left side match the right side.

 Deriving the Pythagorean Identity using the Pythagorean Theorem and the unit circle.

 When verifying identities, it is important to remember that all 6 trig functions can be written using sin and/or cos.

 Verify the following identity by re-writing the left hand side to match the right hand side.

 worksheet 5.1 & 5.2 problems

 Pg 377 (# 50,54,57,58,59)

 As a class, we are going to do the following problems on the board. Volunteers?  p375 #10,13,15,17

 p377 (#45 ̶ 53 odd, 57)

 A ladder leaning against the wall makes an angle of 80* with the ground. If the foot of the ladder is 6ft from the wall, how high is the ladder?

 Your line of sight to the top of a mountain makes a 34* angle with the horizontal. If the line of sight is measured at 5500ft, how tall is the mountain?

 A boy flying a kite lets out 400ft of string which makes an angle of 42* with the ground. Assuming the string is straight and the ground is level, how high above the ground is the kite?

 A wire is attached to the top of a flagpole and is staked to the ground 30ft from its base. If the wire makes a 64* angle with the ground, how tall is the flagpole?

 An airplane climbs at a 9* angle after takeoff. How far has the plane traveled horizontally when it has attained an altitude of 3000ft?

 p377 (#29, 68,69,71,73,77,80, 81,83 #81 & 83)

Four Days

 Applications #1 worksheet

 p394 (#3,9,12,15,19 - 21, 24,25)

 A reference angle is an acute, positive angle formed between the terminal side and the x- axis.

 Sine and Cosine are periodic functions, that is there exists a positive real number k such that f(t+k)=f(t) for every t in the domain of f.

 This video graphs all three functions simultaneously while rotating the angle in standard position on the unit circle.  http://www.dnatube.com/video/12168/Trig- graphs http://www.dnatube.com/video/12168/Trig- graphs

 http://www.touchmathematics.org/topics/tri gonometry http://www.touchmathematics.org/topics/tri gonometry

 Given a trig value, find θ.

 Review 5.1 - 5.3 worksheet

 Find the angle(s) that satisfies each equation:

 Applications worksheet 2 (#1 - 3, 5 – 7)

 A drawbridge is 150ft long across a river. The two sections are of equal length and can be rotated upward to an angle of 35*.  If the water level is 15 feet below the bridge when it is closed. Find the distance between the end of each section of the bridge when raised and the surface of the water.

 A plane is on approach to the Harrisburg Airport at a current elevation of 10000ft. If the plane is 12 miles away what angle of decent should the pilot take to land at the airport?

 Find the height of the Matterhorn.

 Find the distance to the island.

Three Days

 A reference angle is an acute, positive angle formed between the terminal side and the x- axis.

 p404 (#2,3,8 - 18 even(w/out a calculator), 19,21,25,29,33,43)

 Reference angle worksheet  Finish Applications paper #8 plus  p405 #36

 Applications #3 worksheet

Two Days

 p436 (#3,6,11,14,25,27,29,34 exact answers for #3 & 6, look at diagram for 25,29,34)

 p442 (#1 - 4, 7,8,21 - 24, 27,30, 67, 68)

 Prentice Hall p21 (#3,15,16,19,20,25)  No calculator

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