May 18, 2018 · There are multiple ways of proving the identity. Please, see below. First way, probably the more direct method, is by the unit circle: We see that, if we add pi to some angle theta, or in our case, A, |sin theta| = |sin (theta+pi)|, but since thery're on opposite parts of the center O, which is not in the image, they're of opposite sign. color(red)( :. sin(A+pi) = - sinA Another method to ...

Apr 15, 2015 · sin(pi-x) = sin pi cosx -cos pi sinx color(white)"sssssssssss" =(0) cos x - (-1)sinx color(white)"sssssssssss" =sinx Yes.

Apr 7, 2018 · Prove the identity. #sin(pi+x)=-sinx# Have to show the statements and the rules?

Jul 2, 2016 · sin(pi/5)=sqrt(10-2sqrt5)/4 Let theta=pi/5, then 5theta=pi and 3theta=pi-2theta. Note theta) is an acute angle. Hence sin3theta=sin(pi-2theta) but as sin(pi-A)=sinA This can be written as sin3theta=sin2theta expanding them or 3sintheta-4sin^3theta=2sinthetacostheta as theta=pi/5 we have sintheta!=0 and dividing by it we get 3-4sin^2theta=2costheta or 3-4(1-cos^2theta)=2costheta or 4cos^2theta ...

Jul 20, 2017 · Use the identity: sin(A+B) = sin(A)cos(B)+cos(A)sin(B) Substitute x for A and pi for B: sin(x+pi) = sin(x)cos(pi)+cos(x)sin(pi) The second term disappears, because sin(pi) = 0 sin(x+pi) = sin(x)cos(pi) The fact that cos(pi) = -1 finishes the proof: sin(x+pi) = -sin(x) Q.E.D.

Feb 11, 2016 · sqrt(2)/2 In the trigonometric circle pi/4 is the bisectrix between 0 and pi/2, where x=y. By the Pythogoras theorem we know that x^2+y^2=1. If you don't know the trigonometric circle, you can see that if one of the small angles of a rectangle triangle is pi/4, the other will be also pi/4, which implies the catets are equal. So if x=y, you will have x^2+y^2=1 2y^2=1 y^2=1/2 y=sqrt(1/2)=sqrt(2 ...

Apr 13, 2018 · How do you show that #(costheta)(sectheta) = 1# if #theta=pi/4#? See all questions in Trigonometric Functions of Any Angle Impact of this question

Apr 11, 2016 · We want to find replacement angles for # pi/12" that will produce exact values " #. These must come from : # pi/6 , pi/3 , pi/4 #

Mar 15, 2016 · How do you apply the fundamental identities to values of #theta# and show that they are true

Nov 16, 2016 · How do you know if #sin 30 = sin 150#? How do you show that #(costheta)(sectheta) = 1# if #theta=pi/4#? See all questions in Trigonometric Functions of Any Angle