I'm taking on online pre calc class and need help. PLEASE?! Greatly appreciated?

Question

Find tan(sin-1(4/5)).

Find sin(cos-1(-1/5)).

Solve for:

2 cos(x)^2 - 11 cos(x) + 5 = 0

--

I have about 70 of these problems I need to do. I do not know how to solve these kinds of problems. If someone class please show steps Id greatly appreciate it. Gosh. I wish I was good at math

We arent allowed to use calculators though

Answer 1

Arc functions, sometimes denoted with "‾ ¹" are inverse functions.

arcsin[sin(x)] = x
arctan[tan(x)] = x
etc.

Similarly
sin[arcsin(y)] = y

For example
arcsin[sin(π/4)] = π/4
sin[arcsin(1/√2)] = 1/√2

If you have something else like
arcsin[cos(x)]

you have to figure out what sin(x) is. Then you will have an expression of the type arcsin[sin(x)] = x.
______________

Find tan(sin-1(4/5)).
If sin(x) = 4/5 then
cos(x) = √[1 - sin²(x)] = √(1 - 16/25) = √(9/25) = 3/5
tan(x) = sin(x) / cos(x) = (4/5) / (3/5) = 4/3

So we have

tan(sin-1(4/5)) = tan(tan-1(4/3)) = 4/3

The rest will work similarly.

Answer 2

The best advice I can give is that after you get the books or before you need to sit down with a calendar and fill in all your holidays and days off. I try and have my son who is going into 3rd grade have close to the same days off as traditional school. After that we pick a start date and then count the 170 days of requiered school until we come up with an end date. Now for assigning yourself the cource work it is actually already done for you by chapter but here is an easy way. EX there are 36 weeks in the spelling book so that is one chaper a week (exclude the week during the year that only have 2 days) each lesson has 4 pages so 1 page a day and the test on the 5th day. You may have 1 chapter every 2 weeks and a lesson each day do the review questions in each lesson and the additional questions you will do just fine. I have had no help from the local school where I live because 2 educated teachers could not handle 11 kids in grades K-2 so I have homeschooled since we moved here and will continue until we moved. Also the kids in the class we more then a grade below grade level. I still can't figure that one out. Best of luck to you.

Answer 3

1st one:
sin x = 4/5 and x < pi/2 for principal value of arcsin
You can regard 5 as the hypotenuse of a 3-4-5 right angled triangle.
tan x = 4/3

2nd one:
Principal value of arccos(-1/5) is pi - arccos(1/5)
sin(pi - arccos(1/5)) = sin(arccos(1/5))
If x is the angle, then cos x = 1/5, sin x = sqrt(1-(1/5)^2)
= sqrt(24/25) = (2sqrt6)/5

3rd one:
(2cos x - 1)(cos x - 5) = 0
2 cos x = 1 (cos x = 5 not possible)
cos x = 1/2
x = (2n + (1/3))pi or (2n - (1/3))pi

Answer 4

You need a calculator for the first two.

type in 4/5, then press the button "sin-1" or "arcsin".
It will give you a number like 2.8 or something if your your calculator is in radians mode, or something like 140 deg if its in degrees mode.

Now press the button "tan". The new number is your answer.

You should be able to figure out the second one doing similar things.

For the last one:

Factor out the two, or divide everything by two. Now you should have: cos(x)^2 - (11/2)cos(x)+(5/2) = 0

Now divide the equation into two parts: (cos(x) - "blank" )*(cos(x) - "blank"). Next we need to figure out what goes in the blank spots.

If you know how to multiply two things in parentheses, you will know that the two numbers: blank #1 and blank #2 have to multiply to make the number 5/2. You also know that they need to add to -11/2.

Try different numbers until it works!

Answer 5

1. take the arcsin of 4/5 and then find the tangent of that answer
2. take the arccos of -1/5 and then find the sin of that answer
3. simple factoring problem and then solve for x

I