Find the exact values of the following, in surd form form where necessary:
a) sin TT
b) tan TT/4
c) sin 3TT/4
ps. TT is supposed to be pi
2007-10-20 07:25:15 · 8 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
I know it is probably really simple but does anyone have any good websites or explantion on how to get the answers.
2007-10-20 07:38:28 · update #1
this is using radians instead of regular degrees. Using radians, there are 2TT radians in a circle. So TT radians = 180 degrees, 1/2 TT radians = 90 degrees etc. Therefore SinTT = Sin 180 = 0
tan TT/4 = Tan 45 = 1
Sin 3TT/4 = Sin (180-45) = Sin 135 = (1/root 2) OR (root 2/2)
This last answer is to do with using a right-angled triangle. Imagine a right angled triangle with sides 1 and 1, using pythagoras, the last side = root 2. so the Sin is (1/root 2).
This is equivalent to (root 2/2) (multiply top and bottom by root 2 (rationalise the denominator)).
Hope this helps, sorry if its treating u like an idiot, i've no idea how far u are with the work so i tried to cover it all!
2007-10-20 12:12:38 · answer #1 · answered by Ant 2 · 0⤊ 0⤋
The answer about a unit circle is a good one 2pi radians =360 degrees . So pi rads =180 degrees. If you start from a radius of one unit along the x axis on the origin then at 180 degrees it will stretch from x=o to x= -1 and the value of y will be 0 . So clearly sin 180 degrees =0 .
In the pi/4 example . Clearly pi/2 =90 degrees and pi/4 =45 degrees So y =x hence sinpi/4/cospi/4 =1.
3pi/4 will represent 135 degrees. y co-ordinate is positive and it is an isoceles right angled triangle. Pythag gives side as (sq rt(2))/2 =.707 roughly when I was last at school.
2007-10-20 11:31:07 · answer #2 · answered by Anonymous · 0⤊ 1⤋
LoL! that's the best approximation to 'pi' I have ever seen!!
Obv sin(TT)=0, tan(TT/4)=1, sin(3TT/4)=rt(2)/2
just sketch your angles on the quadrant (using TT=180deg) and apply the normal definitions for the different trig functions, taking into account the +/- signs in each quarter.
2007-10-20 09:06:49 · answer #3 · answered by alienfiend1 3 · 0⤊ 1⤋
Sin TT=0
tan TT/4=1
sin 3TT/4=.7071
2007-10-20 07:29:39 · answer #4 · answered by aba 2 · 0⤊ 2⤋
a) sin TT = 0
b) tan TT/4 = 1
c) sin 3TT/4 = {sqrt(2)}/2
2007-10-20 07:29:35 · answer #5 · answered by Anonymous · 0⤊ 1⤋
a)
sin π = 0
b)
tan π/4 = 1
c)
sin 3π/4 = 1 / √2
2007-10-21 02:02:22 · answer #6 · answered by Como 7 · 1⤊ 0⤋
sin(pi) = 0
tan(pi/4) = 1
sin(3pi/4) = SQRT(2)/2.
Now, when you say "exact value", does that mean you want SQRT(2) to a finite number of digits? Can't be done.
2007-10-20 07:30:24 · answer #7 · answered by fcas80 7 · 0⤊ 1⤋
To understand these answers, study the unit circle. It may not be as hard as you think.
a.) 0
b.) 1
c.) sqrt(2) / 2
2007-10-20 07:29:50 · answer #8 · answered by Anonymous · 1⤊ 0⤋