If sin (theta)=3/4, 90 degrees is smaller than (theta) is smaller than 180 degrees, evaluate in surd form,
a. Sin2(theta)
b. cos2(theta)
c.tan2(theta)
In which quadrant does 2(theta) lie in?
The others are quite similar in nature.
If sin (theta)=3/4, 90 degrees is smaller than (theta) is smaller than 180 degrees, evaluate in surd form,
a. Sin2(theta)
b. cos2(theta)
c.tan2(theta)
In which quadrant does 2(theta) lie in?
Thnx
The others are quite similar in nature.
help me pleaseI do not know what I am doing wrong for the following questions:
a. sin4xcos4x
b. 1+cos(180+2(theta))
c.sinxcosxcos2x
d. 2sin2xcos2x
and help me with this one as well(2tantheta)/(1-tan squared theta) when theta = 22.5 degrees
sin squared 50+sin squared 40
(2tantheta)/(1-tan squared theta) when theta = 22.5 degrees
sin squared 50+sin squared 40
Both are clearly equal to 1 (can you see why?).and help me with this one as well
No not quiteBoth are clearly equal to 1 (can you see why?).
First one: double-angle formula for tan, noting tan(45 deg) = 1.No not quite
Thanks integrandFirst one: double-angle formula for tan, noting tan(45 deg) = 1.
Second one: Complementary and Pythagorean trig. identities.
1) Use the identity sin(t)cos(t) = (1/2)*sin(2t).1. sin(45-x)cos(45-x)
2. (1-cos 2theta)/ (1+cos2theta)
3. 2cos squared 3x -1
4. (1-t^2)/(1+t^2) where t=tan theta/2
for 2 and 4 could you please be more clearer1) Use the identity sin(t)cos(t) = (1/2)*sin(2t).
2) Essentially proved here: http://community.boredofstudies.org...do-we-need-memorise-identity.html#post7159341
3) Double angle formula for cos
4) cos(theta)
1) Let t = tan(22.5 deg), then 2t/(1 – t^2) = tan(45 deg) = 1, by the double angle formula.1. Using double angle formula for tan (theta), find tan 22.5 in simplest surd form
2. If tan (alpha)=k tan (beta), show that
(k-1)sin(aplha +beta) = (k+1) sin (alpha - beta)
Tip: If you have cos(2x) by itself then it might be hard to figure out which to use.
Oops I got beaten
for 2 and 4 could you please be more clearer
I was stuck at first and then thought about double angle then when I tried double angle I got some weird answerTip: If you have cos(2x) by itself then it might be hard to figure out which to use.
But if you have 1-cos(2x) try to get used to rewriting as 2sin^2(x)
And 1+cos(2x) as 2cos^2(x)
Just don't forget with cos you have three choices for the double angles. Reason is because of the Pythagorean identity giving you three versionsI was stuck at first and then thought about double angle then when I tried double angle I got some weird answer
Anyways thanks leehuan
yeah I know but which is the best to take?Just don't forget with cos you have three choices for the double angles. Reason is because of the Pythagorean identity giving you three versions
The rule of thumb is when you have 1-cos(2x) you end up with 2sin^2(x)yeah I know but which is the best to take?