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# Dif calc10week1

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### Transcript

• 1. 1. Course Guidelines. 2. Course Procedures. 3. Why do we study Math? 4. Who Am I?
• 2. Factoring Review.
• 3. Opener. 1. What is the ﬁrst step in any factoring problem? 2. What is the ﬁrst step to factor -x2 + 8x - 15? 3. On a test, Luis Gonzalez wrote the following, but the teacher considered it to be incomplete. Explain why. 15x2 - 21x - 18 = (5x + 3)(3x - 6).
• 4. Factoring Strategy. Step 1. Always check for the _________________ ﬁrst. Step 2. Is the expression a -termed expression? If yes, then try one of these three forms: 1. ________________________: 2. ________________________: 3. ________________________: Step 3. If it is a -termed expression (or trinomial), it may fall into one of these groups: 1. The coefﬁcient of is 1. Example: ________________. Find two numbers whose sum is ______ and whose product is ______. They are ______ and ______: 2. The coefﬁcient of is not 1. Example: ________________. a. Find the product of ﬁrst and last coefﬁcients: ___________ = _____. b. Look for two numbers whose product is ______ and whose sum is _____: _____ and ______. c. Write the expression as four terms: d. Proceed to use Step 4 as follows: Step 4. If it is a -termed expression, try factoring by grouping. Example:
• 5. Exercises. Factor each expression completely.
• 6. Homework #1. Baldor, Algebra. Exercise106, Problems 9, 18, 27, 36, 47, 54, 73, 83, 91, 98, 109 and 128, p. 171
• 7. A person is standing at the top of a building, and throws a ball upwards from a height of 60 ft, with an initial velocity of 30 ft per second. How long will it take for the ball to reach a height of 25 ft from the ﬂoor? Use the formula
• 8. Quadratic Formula. If ax2 + bx + c = 0 and a ≠ 1, then
• 9. Exercises. Solve the equations. Use the quadratic formula.
• 10. Homework #2. Baldor, Algebra. Exercise 266, Odd numbered problems, p. 450.
• 11. Opener. 1. Consider equations and Do their solutions have to be the same? Explain your answer. 2. Consider and Are the solutions the same for both equations? Explain. 3. What is a Reference Angle? The Reference angle for θ is the acute angle θR that the terminal side of θ makes with the x-axis.
• 12. Trigonometry Review. Find the reference angle θR for θ, and sketch θ and θR in standard position. a) θ = 315o b) θ = -240o y y x x
• 13. c) θ = 5π/6 y x Multiply degrees by to get radians. Multiply radians by to get degrees.
• 14. Find the exact values of sin θ, cos θ and tan θ if (a) θ = 5π/6 (b) θ = 315o
• 15. Verifying Trigonometric Identities.
• 16. The fundamental identities. 1. The Reciprocal Identities. 2. The Tangent and Cotangent Identities. 3. The Pythagorean Identities.
• 17. Examples. Show that the following equation is an identity by transforming the left-hand side into the right-hand side:
• 18. Exercises.