Warmup 9/3/14

1. Warmup9/3/14 <Write down what you’ve learned from today’s study> Objective Tonight’s Homework To learn rules and identitiesfor angles pp 82: 3, 4, 5, 7, 9

2. Homework Help Let’s spend the first 10 minutes of class going over any problems with which you need help.

3. Notes on Trigonometric Identities Let’s say we wanted to simplify the following problem: sin (θ + π/4) Can we just break it up into sin(θ) + sin(π /4)?

4. Notes on Trigonometric Identities Let’s say we wanted to simplify the following problem: sin (θ + π /4) Can we just break it up into sin(θ) + sin(π /4)? You would think so, but if we tested with some simple angles, we would find this doesn’t work. So how do we solve something like this? There are special formulae we can derive to help us. We’ll derive them later in the year, but for now, we’ll just work with them.

5. Notes on Trigonometric Identities Key Trigonometric Identities tan(θ) = sin(θ) / cos(θ) sin2(θ) + cos2(θ) = 1 sin(A + B) = sin A cos B + cos A sin B sin(A - B) = sin A cos B – cos A sin B cos(A + B) = cos A cos B – sin A sin B cos(A - B) = cos A cos B + sin A sin B

6. Notes on Trigonometric Identities Double-Angle Identities sin(2A) = 2 sin A cos A cos(2A) = cos2 A – sin2 A cos(2A) = 2 cos2 A – 1 cos(2A) = 1 – 2 sin2 A tan(2A) = (2 tan A) / (1 – tan2 A)

7. Notes on Trigonometric Identities Half-Angle Identities sin(x/2) = + √½ - (cos x)/2 cos(x/2) = + √½ + (cos x)/2

8. Notes on Logarithmic Functions Let’s say we wanted to graph log5 x How would we do it?

9. Notes on Logarithmic Functions Let’s say we wanted to graph log5 x How would we do it? If we look at a logarithm and a power function, wesee that they’remirrored.

10. Notes on Logarithmic Functions Let’s say we wanted to graph log5 x How would we do it? If we look at a logarithm and a power function, wesee that they’remirrored. To graph, all we have to do is rearrange it to a power, and swap x and y!

11. Notes on Logarithmic Functions (Follow along with example 12.7 on pp 79) Graph y = log4 x

12. Notes on Logarithmic Functions (Follow along with example 12.7 on pp 79) Graph y = log4 x y = log4 x is mirrored as y = 4x We can flip it back to where it should be by rewriting it as x = 4y.

13. Notes on Logarithmic Functions (Follow along with example 12.7 on pp 79) Graph y = log4 x y = log4 x is mirrored as y = 4x We can flip it back to where it should be by rewriting it as x = 4y. Let’s solve x = 4y at afew points to get a feelfor a few points on thegraph.

14. Notes on Logarithmic Functions (Follow along with example 12.7 on pp 79) Graph y = log4 x y = log4 x is mirrored as y = 4x We can flip it back to where it should be by rewriting it as x = 4y. Let’s solve x = 4y at afew points to get a feelfor a few points on thegraph.

15. Notes on Logarithmic Functions (Follow along with example 12.7 on pp 79) Graph y = log4 x y = log4 x is mirrored as y = 4x We can flip it back to where it should be by rewriting it as x = 4y. Let’s solve x = 4y at afew points to get a feelfor a few points on thegraph.

16. Notes on Logarithmic Functions (Follow along with example 12.7 on pp 79) Graph y = log4 x y = log4 x is the same as x = 4y Let’s solve x = 4y at afew points to get a feelfor a few points on thegraph.

17. Notes on Logarithmic Functions If we have a problem with a negative log, just switch the negative to the y, then solve the same way. y = -log x | | V -y = log x

18. Group Practice Look at the example problems on pages 75 through 81. Make sure the examples make sense. Work through them with a friend. Then look at the homework tonight and see if there are any problems you think will be hard. Now is the time to ask a friend or the teacher for help! pp 82: 3, 4, 5, 7, 9

19. Exit Question #6 Without using a calculator, find the exact value for… tan (45) a) 1 b) 3.14 c) infinite d) 0 e) 1.57 f) 0.707