2018年4月13日 · sqrt2/2 As you can see in the table above, cos45^@ or cospi/4 radians is the same thing as sqrt2/2 An alternative way is looking at the unit circle: We know that the cosine of an angle is the x-value of a coordinate. At pi/4, we can see that the x-value is sqrt2/2. Therefore, cos(pi/4) = sqrt2/2 Hope this helps!

2018年3月7日 · #cos(pi/4)=sqrt(2)/2#, refer to the explanation below for how to find the exact value without a calculator. Explanation: It is possible to find the exact value of #cos(pi/4)# by constructing a right triangle with one angle set to #pi/4# radians.

2016年4月4日 · Let's first convert to degrees. The conversion ratio between degrees and radians is 180/pi. pi/4 xx 180/pi = 45^@ Now, we must think of the special triangle that contains a 45^@ angle. This would be the following triangle. The definition of cos is adjacent/hypotenuse. Therefore, our ratio is 1/sqrt(2). However, often, teachers want the denominator to be rationalized, or be a rational number ...

2015年7月29日 · The restriction to angles between #0# and #pi# makes #arccos# a function. #arccos(cos((5pi)/4))# is an angle between #0# and #pi# whose cosine is the same as the cosine of #(5pi)/4#. The angle we want is #(3pi)/4# We know that #cos((5pi)/4) = -sqrt2/2# and the Quadrant II angle with cosine equal to #-sqrt2/2# is #(3pi)/4#

2016年6月25日 · cos((15pi)/4) = cos(2*(2pi)-pi/4) = cos(-pi/4) = 1/sqrt(2) = sqrt(2)/2~=0.7071 We can look at this by considering the angle on the unit circle, where cos is the projection on the x-axis: graph{(y^2+x^2-1)((y+0.7071)^2+(x-0.7071)^2-.001)((y)^2+(x-0.7071)^2-.001)=0 [-2.434, 2.433, -1.215, 1.217]} From this it is easy to see that the same value repeats itself for each full revolution on the ...

2015年8月12日 · cos((11pi)/4)=-(sqrt(2))/2 First we have to notice, that (11pi)/4 >2pi, so we can use this to reduce the angle, because cos(2pi+x)=cos(x) After this reduction we have to calculate cos((3pi)/4).

2017年2月2日 · cos^-1 (cos(-pi/4)) =pi/4 pi=180^0 :. pi/4= 180/4=45^0 cos^-1 (cos(-pi/4)) = cos^-1 (cos(-45)) = cos^-1 (cos(45)) [since cos(-theta)= cos theta]. Let cos^-1 (cos 45 ...

2015年4月26日 · arccos(cos(4)) is a value, t between 0 and pi whose cosine is equal to the cosine of 4. Note that 4> pi, but 4 <= (3 pi)/2 ~~ 9.42/2 = 4.71. Thinking of t=4 as the radian measure of an angle, it corresponds to an angle in quadrant 3. and the reference angle is 4 - pi. The second quadrant angle with the same reference angle is pi - (4-pi) , which is 2 pi - 4 So arccos(cos(4)) = 2 pi -4 Note All ...

Dividing by #4# (multiplying by #1/4#) gets us to: #x= pi/8+(2pi k)/4# or #x=(7 pi)/24+(2 pi k)/4# for integer #k#. We can write this in simpler form: #x= pi/8+pi/2 k# or #x=(7 pi)/24+pi/2 k# for integer #k#. Final note The Integer #k# could be a positive or negative whole number or 0. If #k# is negative, we're actually subtracting from the ...

2018年7月24日 · We have, #cos(pi/2^2)cos(pi/2^3)cos(pi/2^4)...cos(pi/2^2006)=2^-acos(pi/b)#. Observe that, there are #2005# terms on the L.H.S. of this eqn.