1)Express the function y=cos\theta + sin\theta in the form
y = sqrt(2)[cos(theta)/sqrt(20 - sin(theta)sqrt(2)
= sqrt(2)[cos(theta-pi/4)
2) 2(arccos(x) = theta
arccos(x) = theta/2
(x) = cos(theta/2)
cos(theta) = 2cos^2(theta/2) - 1 = 2x^2 -1
Hi
I need help on the following question:
1)Express the function y=cos\theta + sin\theta in the form
2)Express the following as algebraic expressions in terms of x:
This is what i have done, but i don't understand how this is incorrect.
so that means
P.S
1)Express the function y=cos\theta + sin\theta in the form
y = sqrt(2)[cos(theta)/sqrt(20 - sin(theta)sqrt(2)
= sqrt(2)[cos(theta-pi/4)
2) 2(arccos(x) = theta
arccos(x) = theta/2
(x) = cos(theta/2)
cos(theta) = 2cos^2(theta/2) - 1 = 2x^2 -1
Hello PaymemoneyLetExpand the RHS using the formula :
Now compare the coefficients of and on both sides of the equation:
Square (1) and (2) and add, noting that :
Divide (2) by (1):
Substituting these values of and back into the original equation gives:
Let2)Express the following as algebraic expressions in terms of x:Then:Also:
...(3)
Grandad
, using the formula
, from (3)
Hello PaymemoneyOK. Let's see if we can make it easier. I'll set it out slightly differently.
LetNow means 'the angle whose cosine is ...'. Someans
the angle whose cosine is isIn other words
, which I'll call equation (1)Now the question asks us for
In other words, forSo we use the well-known double angle formula
and then use equation (1) to replace by . So we get:OK now?
I'm not sure why you should think this. This would mean that if you double an angle you double its cosine. So would equal . Which it doesn't, does it?
Grandad