Questions on Algebra: Trigonometry answered by real tutors!

You can put this solution on YOUR website!
cos2x + cos x
replace cos 2x with 2cos^2-1
2cos^2-1 + cos x = 0
Rearrange
2cos^2x + cos x - 1 = 0
(2cosx - 1)(cosx + 1) = 0
cosx = 1/2 or -1

x = 60 degs, 300degs and 180degs
= pi/3 rads, 5pi/3 rads and pi

You can put this solution on YOUR website!
Do you want this equation solved?
If so:
2tanx + 2 = 4
2tanx = 4 - 2
2tanx = 2
tanx =2/2
tanx = 1
x = 45 degrees, 225 degrees
= 0.78 rads , 3.92 rads

You can put this solution on YOUR website!
the second part sounds like it's a lot easier than the first part.
all you need to do is find the cosine of 40 degrees and replace x in the equation.
if the value of the equation comes out to be equal to 0, then cosine of 40 degrees is a root of the equation since the roots of the equation are when the value of y is equal to 0.
use your calculator to find cosine of 40 degrees.
that turns out to be equal to be equal to .766044443.
store that in your memory so as not to get rounding errors and use that stored result in place of x in the equation.
when you replace x in your equation with the stored value of .766044443, the result is 0 indicating that cosine of 40 degrees is a root of the equation.
alternately, you can graph your equation and find the roots (when the equation crosses the s-axis are the roots).
the graph of the equation actually crosses the x-axis in 3 places, and the third place (the rightmost intersection) is equal to the cosine of 40 degrees (.76604443).
the graph of the equation is shown below:
i drew a vertical line (well, almost vertical) at x = .766044443 to show you that the graph of the equation crosses the x-axis at that point.

You can put this solution on YOUR website!
Verify:
start with LHS


verified: LHS=RHS

You can put this solution on YOUR website!
No. Actually, the formula for sin(a+b) IS the shortcut. For a quick reference see the Angle Sum and Difference Identities in http://en.wikipedia.org/wiki/Angle_sum_formula#Angle_sum_and_difference_identities

You can put this solution on YOUR website!
If sin(theta)= (sqrt2)/5, and pi/2 < theta < pi, then find the exact value of tan(2theta) using identities
***
Identity:
..


Identity:

..
Check with calculator:
sin(x)=√2/5
x≈16.43º
2x≈32.86º
tan(2x)=tan(32.86º)≈0.6459
exact value=≈0.6459

You can put this solution on YOUR website!
Assuming you mean




we can write


then

then



and finally



:)

You can put this solution on YOUR website!
Verify: (sec(x)/sin(x))-(sin(x)/cos(x))=cot(x)
-----
(1/(cos*sin)) - (sin/cos) = (cos/sin)
----
Multiply thru by cos*sin to get:
1 - sin^2 = cos^2
---
cos^2 = cos^2
=================
Cheers,
Stan H.
===============

A=[1 -1  0] 
  [1  0 -1]  
  [6 -2 -3] 

B=[-2 -3 1]
  [-3 -3 1]
  [-2 -4 1]

     

Consider the minus sign before the 4 as a plus sign times (-4).
That's because we'd rather add matrices than subtract them:

     

Substitute the matrices in the equation for the letters:

 

Distribute the (-4) by multiplying it by all 9 elements of the 
matrix on the far right:

 

We add the corresponding elements of the matrices on the right:

 

Finally we multiply both sides by 




Distribute the  by multiplying it by all 9 elements of the 
matrix on the right:

   

Edwin