april fool's blog

since we just reviewed this week on ch 7 and ch8 i will go over some important stuff in ch 7. the main thing in ch 7 is converting degrees to radians and radians to degrees. now there are two formulas to do this. the first formula is degrees to radians. basically all you do is do the (degrees) * (pi)/180 or you can just do (degrees) / 180 and put pi next to it. to convert from radians to degrees is simple. the formula is radians * 180/(pi). in most cases pi will cancel and kleave you with a degree put sometimes it will not. examples will be listed below.

EX: convert 196 (degrees) to radians
196 / 180 (pi)
= 49(pi) / 45


b) convert 3(pi) / 4 to dergees
3(pi) / 4 * 180 / (pi)
pi's cancel
=3/4 * 180
= 135 (degrees)

Degrees - Rads and vice versa

To convert from degrees to radians, divide the degree by 180 and add pie behind the coefficient.
To convert from radians to degrees, multiply the number in radians by 180 and take out the pie.

Degrees to Rads:
180degrees: 180/180 = 1pie
360degrees: 360/180 = 2pie
Radians to Degrees:
1pie: (1pie)(180) = 180degrees
2pie: (2pie)(180) = 360degrees

P.S. Happy Birthday to me haah

7-1 Review

This weekend I am going to review with you all the information that we learned in Chapter 7 section 1. This lesson is about degrees, radians, and co-terminal angles. In this lesson we learned how to convert degrees to radians and radians to degrees. We also learned how to convert degrees to minutes and seconds and how to find co-terminal angles.

Notes:

• When you convert from degrees to radians, you use this formula: degrees * pi/180
• When you convert from radians to degrees, you use this formula: radians * 180/pi
• To convert from degrees to minutes and seconds, you take what is behind the decimal and multiply it by 60. Then you would do it again to find seconds. If there is still a decimal, then you drop the numbers after the decimal
• To convert from minutes and seconds back to degrees follow this formula:
Degrees + min/60 + sec/3600
• When you find a co-terminal angle, you add/subtract 360 degrees or 2 pi

Example: convert 60 degrees to radians
• 60 * pi/180
• 60 pi/180
• Pi/3


-Braxton-

8-4 Review

Things you should know:

• Do all the possible algebra in the problem first.
• After you do everything possible, you should use the Pythagorean identities.
• After you do that you should move everything to sin and cos.
• After that you should do algebra again.
• Once you do all of those steps, you repeat steps 1-3 until the problem is simplified

• Pythagorean Identities:

1. sin^2x + cos^2x = 1
2. 1 + tan^2x = sec^2x
3. 1 + cot^2x = csc^2x

• Changing to sin to cos:

1. cscx = 1/sinx
2. tanx = sinx/cosx
3. cotx = cosx/sinx
4. secx = 1/cosx

Example 1: cos^2x - 1

• You can not do any algebra in this problem.
• If you noticed, this problem is part of your Pythagorean identities
• Since we know sin^2x + cos^2x = 1 then we know cos^2x - 1 = sin^2x.
• Final answer: sin^2x.

Example 2: 1 + cot^2x

• This is the same thing as the last example.
• You can not do any algebra in this problem.
• This problem is part of your Pythagorean identities.
• 1 + cot^2x = csc^2x
• Final answer: csc^2x

-Amber :)

7-1

Since we've been doing trig review I'm gonna go over 7-1. This section is about converting degrees to radians, radians to degrees, and how to find co-terminal angles.

When you are converting from degrees to radians you use the formula degrees*pi/180

When you are converting from radians to degrees you use the formula radians*180/pi

When you convert from radians to degrees and you have to find minutes, you take what's behind the decimal and multiply it by 60. If you have to find seconds then you use what's behind the decimal after you find minutes and multiply it by 60. If there is a decimal, just drop what's behind it.

To convert back to degrees, you use this formula: degrees+min/60+sec/3600

To find a co-terminal angle, you add or subtract 360 if in degrees, or add or subtract 2pi if in radians.

example 1:

Convert 200 degrees to radians

200*pi/180

10 pi/9

example 2:

convert 5 pi/9 to degrees

5 pi/9 * 180/ pi

the pis cancel

100 degrees

Review of 8-4

Okay so this week I am going to review section 8-4 which is on the relationship among functions! This was confusing when I first learned it, but it is actually very easy once you remember all the relationships. So first I am going to give you a few notes that you are going to need.

Notes:

• The first thing you do is to do all the possible algebra to the problem.
• Once you do everything possible, you would first try to use your pythagorean identities.
• After that you would move everything to sin and cos.
• The next thing you would do is do algebra again.
• Once you do all of that you keep repeating steps 1 through 3 until your problem is completely simplified.

Okay, so now that you know all that, I am going to give you a few extra things you are going to need to know.

Pythagorean Identities:

• sin^2x+cos^2x=1
• 1+tan^2x=sec^2x
• 1+cot^2x=csc^2x
  

Changing to Sin and Cos

• cscx=1/sinx
• tanx=sinx/cosx
• cotx=cosx/sinx
• secx=1/cosx

Now that you know everything you need to know, I will work a few examples for you. This is hopefully help you to better understand how to work these problems.

Example 1: 1+tan^2x

• There is no possible algebra that can be done to this problem.
• This problem is one of your pythagorean identities, which is going to make your problem equal to secx^2. That is then going to be your answer.
• So you answer is secx^2.

Example 2: cos^2x+sin^2x

• There is no possible algebra that can be done to this problem.
• You are first going to look for identities, which you can tell that this problem is one of the
• pythagorean identities which means it will equal to 1.
• So you answer is going to be 1.

And that is it for this weeek. See youu next weeek. Byeee.

--Halie!

7-1

Review of 7-1

This week I'm going to do a review on lesson 7-1 since we've been doing trig review all week. In this lesson, we learn how to convert degrees to radians, radians to degrees, degrees to minutes and seconds, and minutes and seconds to degrees. We also learned how to find co-terminal angles.

- To convert degrees to radians: degrees x pi/180 (In the calc, you type degrees/180, and convert to a fraction, then put pi beside it.

- To convert radians to degrees: radians x 180/pi (Pi will cancel out)

- To covert degrees to minutes and seconds: For minutes, you take what is behind the decimal and multiply by 60. Once you get that answer, you take what is behind the decimal and multiply by 60 which will give you your seconds.

- To convert from minutes and seconds to degrees: degrees + min/60 + sec/3600

- To find a co-terminal angle: n +/- 360 degrees

Example 1:

a) convert 315 degrees to radians: 315 degrees x pi/180

= 7pi/4

b) convert -pi/2 to degrees: -pi/2 x 180/pi

= -90 degrees

c) convert 1.32 to degrees, minutes, and seconds: 1.32 x 180/pi

= 75.630 degrees

- .630 x 60 = 37.8 minutes

- .8 x 60 = 48 seconds

= 75 degrees, 37 minutes, 48 seconds

Example 2:

a) Find a positive co-terminal angle to -100 degrees: -100 + 360

= 260 degrees

b) Find a negative co-terminal angle to 500 degrees: 500 - 360(2)

= -220 degrees