Day 9-3 Notes
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This document provides instructions and examples for finding trigonometric functions like sine, cosine, and tangent for various angles. It asks the reader to find the exact values of trig functions for angles including 30°, 45°, 60°, 90°, and 0°. Examples are given for finding the cosine and sine of unspecified angles and for sketching angles and finding their reference angles.
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This document contains a graph with labeled x and y axes ranging from -6 to 6. Within this range are curved lines forming a circle centered at the point (4, 1).
Day 2 And 3 Midpoint And Slope
The document provides formulas and examples for calculating slope and midpoints of lines and determining properties of triangles. It includes the slope formula, definitions for lines with the same or opposite reciprocal slopes, the midpoint formula, an example of finding the other endpoint given one endpoint and the midpoint, and an example of proving a triangle is isosceles and right using its vertex coordinates.
Lsn 12-1: The Distance Formula
To find the distance between points G(-5, -8) and H(3,7) use the distance formula. Also use the distance formula to find the distance between points L(15, 37) and M(42, 73). The distance formula is used to calculate the distance between the points (-19, -16) and (-3, 14).
Lsn 13-1: Function Translations
The passage discusses the importance of summarization in efficiently conveying key information from lengthy documents. It notes that effective summaries distill the most critical details and events into a brief yet informative recap of the overall topic and narrative. The ability to produce high-quality summaries is a useful skill for professionals across many fields in order to save time and focus on the most pertinent details.
Lsn 11 12 Kites
This document contains numerical values for variables a, b, c, and d in two sections about arithmetic and midsegments. In the arithmetic section, the values are 42, 63, 117, and 14 for the first line, and 30, 28.5, 87, and 12 for the second line. In the algebra section, x is given as 6 for the first two lines, but no values are provided for the third line.
Lsn 11-12: Kites
This document contains numerical values for variables a, b, c, and d in two sections about arithmetic and midsegments. In the arithmetic section, the values are 42, 63, 117, and 14 for the first line, and 30, 28.5, 87, and 12 for the second line. In the algebra section, x is given as 6 for the first two lines, but no values are provided for the third line.
Lsn 11-10: Applications & Regents Problems
This document contains 3 trigonometry word problems: 1) Find the length of a segment labeled x in a diagram with a 12 foot side. 2) Given a 46 foot sign on a building, find the height of the building using angles of elevation. 3) Given angles of elevation to a lighthouse from a ship and its distance traveled, find how close the ship is to dangerous rocks near the lighthouse.
Lsn 11-6: Law of Cosines
The document provides examples of using the Law of Sines and Law of Cosines to solve for missing sides and angles of triangles. It includes 5 multi-step triangle problems worked out using the two trigonometric laws, with the key points being that Law of Sines is used when an angle is given alone, Law of Cosines is used when a side is given alone or one triangle has a right angle, and letter assignments in the Law of Cosines formula can be changed.
Lsn 11-7: Law of Cosines to find an Angle
The document provides 3 examples of using the Law of Cosines to find the measure of an angle given the lengths of 3 sides of a triangle. The first example finds the measure of an acute angle C in a triangle with sides of lengths 5, 12, and 9. The second finds the right angle C in a triangle with sides of lengths 5, 12, and 13. The third finds the measure of an obtuse angle C in a triangle with sides of lengths 5, 12, and 15.
Lsn 11-5: Law of Sines
Here are the steps to solve these Law of Sines problems:
1. Given: a = 13, b = 20, A = 75°
Use the Law of Sines: sin(A)/a = sin(B)/b
sin(75°)/13 = sin(B)/20
sin(75°)*20/13 = sin(B)
B = sin-1(0.8) = 67°
2. Given: a = 25, B = 38°
Use the Law of Sines: sin(A)/a = sin(B)/b
sin(38°)/25 = sin(m°)/20
sin(38°)*20/25 = sin
Lsn 11-8: Proving a Rhombus/Rectangle
To prove that a quadrilateral is a rectangle or rhombus, you must first prove that it is a parallelogram by showing that both pairs of opposite sides are parallel and congruent. Then, you need only one additional condition - either that the diagonals are congruent (rectangle) or that one angle is a right angle (rectangle), or that the diagonals are the same length (rhombus) or that one pair of consecutive sides are congruent (rhombus). The document provides an example proof of showing a quadrilateral is a rectangle.
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- 2. Find the exact value of each of the following. P (x,y) sin 300 = 300 cos 300 = 0 O D (1,0) tan 30 = P (x,y) sin 600 = 600 cos 600 = O D (1,0) tan 600 = P (x,y) sin 450 = 450 cos 450 = O D (1,0) tan 450 =
- 3. P (x,y) 0 sin 90 = cos 900 = 900 tan 900 = O D (1,0) 0 sin 0 = cos 00 = 00 P (x,y) tan 00 = O D (1,0)
- 4. (in degrees)
- 6. Examples: Sketch each angle. Then find its reference angle. 0 0 1. 300 2. 195
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