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cos(pi-x)= -1cosx

2007-04-02 18:00:00 · 3 answers · asked by Sophia D 1 in Science & Mathematics Mathematics

3 answers

Use the rule for cos of a sum.
cos(A+B) = cos A cos B − sin A sin B

Substitute pi for A and x for B and you get
cos(pi+x) = cos pi cos x − sin pi sin x

cos(pi)=-1 and sin(pi) =0 so the sinpi sinx drops out leaving just
=-1cosx

2007-04-02 18:12:48 · answer #1 · answered by Rich 2 · 0 0

Construct a unit circle. Pick an angle x (preferably less than pi/2), construct cos(pi-x) on the unit circle as well as cos(x). It is evident that the value of cos(pi-x) is negative while that of cos(x) is positive.

2007-04-03 01:09:48 · answer #2 · answered by cattbarf 7 · 0 0

Use the angle addition formula: cos(a+b) = cos(a)cos(b)-sin(a)sin(b) let a= pi and b=(-x)

this gives cos(pi)cos(-x) - sin(pi)sin(-x)
sin(pi)=0, cos(-x) = -cos(x)
This gives u the identity

2007-04-03 01:13:17 · answer #3 · answered by J 2 · 0 0

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