1 The Six Trigonometric Functions 2 Right Triangle Trigonometry 3 Radian Measure 4 Graphing And Inverse Functions 5 Identities And Formulas 6 Equations 7 Triangles 8 Complex Numbers And Polarcoordinates A Appendix: Review Topics Chapter1: The Six Trigonometric Functions
1.1 Angles, Degrees, And Special Triangles 1.2 The Rectangular Coordinate System 1.3 Definition I: Trigonometric Functions 1.4 Introduction To Identities 1.5 More On Identities Chapter Questions Section1.2: The Rectangular Coordinate System
Problem 1PS: For Questions 1 through 6, fill in each blank with the appropriate word or expression. The Cartesian... Problem 2PS Problem 3PS Problem 4PS: For Questions 1 through 6, fill in each blank with the appropriate word or expression. The notation... Problem 5PS Problem 6PS Problem 7PS: State the formula for the distance between (x1, y1) and (x2, y2). Problem 8PS Problem 9PS Problem 10PS Problem 11PS Problem 12PS: Determine which quadrant contains each of the following points. (1,3) Problem 13PS Problem 14PS: Graph each of the following lines. y=x Problem 15PS Problem 16PS Problem 17PS Problem 18PS Problem 19PS: For points (x. y) in quadrant I the ratio x/y is always positive because x and y are always... Problem 20PS Problem 21PS: Graph each of the fo1lowing parabolas. y=x24 Problem 22PS Problem 23PS Problem 24PS Problem 25PS: Use your graphing calculator to graph y=ax2 for a=110,15,1,5, and 10. Copy all five graphs onto a... Problem 26PS Problem 27PS: Use your graphing calculator to graph y=(xh)2 for h = –3.0, and 3. Copy all three graphs onto a... Problem 28PS: Use your graphing calculator to graph y=x2+k for k=3,0, and 3. Copy all three graphs onto a single... Problem 29PS Problem 30PS: Human Cannonball Referring to Problem 29, find the height reached by the human cannonball after he... Problem 31PS Problem 32PS Problem 33PS Problem 34PS Problem 35PS Problem 36PS Problem 37PS Problem 38PS: Find the distance from the origin out to the point (–5, 5). Problem 39PS Problem 40PS Problem 41PS: Pythagorean Theorem An airplane is approaching Los Angeles International Airport at an altitude of... Problem 42PS: Softball Diamond In softball, the distance from home plate to first base is 60 feet, as is the... Problem 43PS: Softball and Rectangular Coordinates If a coordinate system is superimposed on the softball diamond... Problem 44PS: Softball and Rectangular Coordinates If a coordinate system is superimposed on the softball diamond... Problem 45PS Problem 46PS Problem 47PS Problem 48PS Problem 49PS Problem 50PS Problem 51PS Problem 52PS: Graph the circle x2+y2=1 with your graphing calculator. Use the feature on your calculator that... Problem 53PS: Graph the circle x2+y2=1 with your graphing calculator. Use the feature on your calculator that... Problem 54PS Problem 55PS Problem 56PS Problem 57PS Problem 58PS: Use the graph of Problem 50 to name the points at which the line x – y = 6 will intersect the... Problem 59PS Problem 60PS Problem 61PS Problem 62PS Problem 63PS Problem 64PS Problem 65PS Problem 66PS Problem 67PS Problem 68PS Problem 69PS: Use Figure 24 for Problems 61 through 72. Figure 24 Name an angle between 0 and 360 that is... Problem 70PS Problem 71PS: Use Figure 24 for Problems 61 through 72. Figure 24 Name an angle between 0 and 360 that is... Problem 72PS Problem 73PS: Draw each of the following angles in standard position, and find one positive angle and one negative... Problem 74PS Problem 75PS Problem 76PS Problem 77PS: Draw each of the following angles in standard position and then do the following: a. Name a point on... Problem 78PS Problem 79PS: Draw each of the following angles in standard position and then do the following: a. Name a point on... Problem 80PS: Draw each of the following angles in standard position and then do the following: a. Name a point on... Problem 81PS Problem 82PS Problem 83PS Problem 84PS: Draw each of the following angles in standard position and then do the following: a. Name a point on... Problem 85PS Problem 86PS: Find all angles that are coterminal with the given angle. 60 Problem 87PS Problem 88PS: Find all angles that are coterminal with the given angle. 180 Problem 89PS: Draw 30 in standard position. Then find a if the point (a, 1) is on the terminal side of 30. Problem 90PS: Draw 60 in standard position. Then find b if the point (2, b) is on the terminal side of 60. Problem 91PS: Draw an angle in standard position whose terminal side contains the point (3, –2). Find the... Problem 92PS: Draw an angle in standard position whose terminal side contains the point (2, –3). Find the... Problem 93PS Problem 94PS Problem 95PS Problem 96PS Problem 97PS Problem 98PS Problem 99PS: To draw 140 in standard position, place the vertex at the origin and draw the terminal side 140... Problem 100PS: Which angle is coterminal with 160 ? a. 50 b. –70 c. 20 d. –200 Problem 90PS: Draw 60 in standard position. Then find b if the point (2, b) is on the terminal side of 60.
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Use a 30-60-90 triangle to find the cosine of 60∘.
Transcribed Image Text: **Question 12:** Use a 30–60–90 triangle to find the cosine of 60°.
**Options:**
- \(\sqrt{3}\)
- \(\frac{2\sqrt{3}}{3}\)
- \(\frac{\sqrt{3}}{2}\)
- \(\frac{1}{2}\)
**Explanation:** In a 30–60–90 triangle, the sides are in the ratio 1 : \(\sqrt{3}\) : 2. The cosine of 60° is the ratio of the adjacent side to the hypotenuse, which is \(\frac{1}{2}\).
Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).
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