Ms. Armstrong gave us a yellow sheet of paper with 2 questions on it. The first question didn't make sense at all so even Ms. Armstrong had some confusion. So we'll omit that so we can focus on the more important stuff.

**a) sin(x) = .707**acute angle = ___ obtuse angle = ___

**b) cos(x) = .940**acute angle = ___ obtuse angle = ___

**c) tan(x) = 11.43**acute angle = ___ obtuse angle = ___

**d) cos(x) = -.970**acute angle = ___ obtuse angle = ___

**e) sin(x) = -.5**acute angle = ___ obtuse angle = ___

**f) tan(x) = -1.43**acute angle = ___ obtuse angle = ___

**Note:**It's not as easy at it looks. Here's how you solve each of the above questions but first, keep in mind to

*round all of your degrees to a whole number*.

1) To find the

**acute angle**, punch in the equation in your calculator:

**2nd function > SIN/COS/TAN button = SIN/COS/TAN**.

^{-1}(given ratio)Let's use letter a) for an example.

So, 2nd funct. > SIN button = SIN

^{-1}(.707) : the answer is 45

^{o}.

**The degree that comes out of this equation is your acute angle.**

2) Now let's find the

**obtuse angle**. To find the obtuse angle, you will need to know which quadrant does the given ratio belongs to.

**positive cosine ratio**belongs to the first and fourth quadrants

**positive tangent ratio**belongs to the first and third quadrant.

**positive sine ratio**lands on the 2nd quadrant, you have to

**s**ubtract your acute angle from 180 degrees since the acute angle is the measurement of how far is your hypoteneuse from the 2nd quadrant's degree (which is 180 degrees).

**positive cosine ratio**, subtract

**the acute angle from 360 degrees since it lands on the 4th quadrant.**

**positive tangent ratio**, subtract the acute angle from 270 degrees or add the acute angle to 180 degrees.

And now you're done your positive ratios! Here's how I solved the first three questions:

**a) sin(x) = .707**which is 45

^{o}.

^{o}

**acute angle**= 45

^{o}

**obtuse angle**= 135

^{o}

^{}

^{}

^{}

^{}

^{}

^{}

**b) cos(x) = .940**which is 20

^{o}

^{o}

^{}

**acute angle**= 20

^{o}

**obtuse angle**= 34

^{o}

^{}

^{}

^{}

^{}

^{}

^{}

**c) tan(x) = 11.43**which is 85

^{o}

**acute angle**= 85

^{o}

**obtuse angle**= 265

^{o}

^{}

^{}

**negatives**(questions 4 - 6). The negative ratios are a little bit different.

**acute angle**of a

**negative ratio**, do the same thing as how you would find the acute angle of a positive ratio, here's a refresher:

**2nd function > SIN/COS/TAN button = SIN/COS/TAN**

^{-1}(given ratio).^{-1}(-.970)

**-166 degrees**. But that's the not the final answer.

*Remember, the acute angle should be positive*. So the answer will be 166 degrees (yes, just randomly take out the negative sign because I don't think that there is a mathematical format for how to change a negative degree to a positive degree).

2) Then let's find the obtuse angle. Do the same thing as you did to the positive ratios.**d) cos(x) = -.970** which is 166 degrees**acute angle =** 166 degrees**obtuse angle =** 194 degrees**e) sin(x) = -.5** which is 30 degrees**acute angle =** 30 degrees**obtuse angle =** 330 degrees**f) tan(x) = -1.43** which is 55 degrees**acute angle =** 55 degrees**obtuse angle =** 235 degrees

And that's it! Sorry for the delay guys, there was too much in my head, although it's done now (: we also got our unit tests back then we went over some of the questions. Congratulations to the all stars! And oh yeah, I pick **Desitini** to blog next since the people I know didn't want to since they're "busy", haha. Oh yeah, and **reminder** to redo question #2 on exercise 18 using the above steps.

Ms. Armstrong, a video for this one is kind of hard to find. If anyone can help me , that'll be great :)