Norm was fourth at the 2004 USA Weightlifting Nationals! that still trains and competes occasionally, in spite of his busy schedule.
You are watching: Cos(pi/2-x)=sinx
:Applying the cosine enhancement and sine addition formulas proves the cofunction, include pi, and also supplementary angle identities. Utilizing the formulas, we view that sin(pi/2-x) = cos(x), cos(pi/2-x) = sin(x); that sin(x + pi) = -sin(x), cos(x + pi) = -cos(x); and that sin(pi-x) = sin(x), cos( -x) = -cos(x). The formulas additionally give the tangent the a difference formula, because that tan(alpha-beta).
Let's review the cosine addition formulas and the sine enhancement formulas. By cosine addition formulas I median both the cosine that a sum and a cosine of the difference and remember the for both of these it's cosine cosine, sine sine. Cosine alpha cosine beta, sine alpha sine beta. With the cosine the a sum, you change the sine with cosine you always adjust sine think c means change, again cosine cosine, sine sine, the minus i do not care plus. Now for the sine enhancement formulas, it's sine cosine cosine sine, therefore sine alpha cosine beta, it's beta, cosine alpha sine beta and also the sine continues to be the exact same think s because that the exact same plus sine alpha cosine beta cosine alpha sine beta minus stays minus. Therefore these room the cosine addition formulas and also the sine enhancement formulas.And what's really us neat about these is an addition of gift able come calculate specific values of details special angles. We have the right to use these to prove identities and I want to begin with the cofunction identities because that an example. Now you probably currently know these identities yet it's good to help you remember lock to be able to prove them utilizing the sine addition or subtraction formulas, for this reason the sine the pi end 2 minus theta. This is this is going to give us a cofunction identity, let's use the sine of a distinction formula. It's sine cosine, sine pi over 2 cosine theta cosine sine, cosine pi over 2 sine theta because it's minus and also sine sine states the same, we have actually a minus. Currently sine pi over 2 is 1 times cosine theta, cosine pi over 2 is 0, 0 times sine theta for this reason this just becomes cosine theta and that's the formula we'll remember. Sine of pi over 2 minus theta amounts to cosine theta.Likewise here's cosine pi end 2 minus theta, the cosine of a difference formula is what we need here. The cosine of a distinction formula goes cosine cosine sine sine. Cosine pi end 2 cosine theta sine pi over 2 sine theta and cosine the sines change c for adjust so minus becomes plus.
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Psychic cosine of pi end 2 0 sine of pi end 2 is 1 and so we end up through sine theta. Cosine the pi over 2 minus theta equates to sine theta, for this reason the cosine and sine addition formulas room really helpful for proving identities.