Norm was 4th at the 2004 USA Weightlifting Nationals! He still trains and competes occasionally, despite his busy schedule.




You are watching: Sin(pi/2-x)

:Applying the cosine addition and sine enhancement formulas proves the coattribute, add pi, and also supplementary angle identities. Using the formulas, we check out 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 likewise give the tangent of a difference formula, for tan(alpha-beta).


Let's review the cosine enhancement formulas and the sine enhancement formulas. By cosine addition formulas I expect both the cosine of a amount and a cosine of the difference and also remember that for both of these it's cosine cosine, sine sine. Cosine alpha cosine beta, sine alpha sine beta. With the cosine of a amount, you change the sine via cosine you always adjust sine think c represents readjust, aobtain cosine cosine, sine sine, the minus becomes plus. Now for the sine addition formulas, it's sine cosine cosine sine, so sine alpha cosine beta, it's beta, cosine alpha sine beta and also the sine stays the same think s for the same plus sine alpha cosine beta cosine alpha sine beta minus continues to be minus. So these are the cosine enhancement formulas and also the sine enhancement formulas.And what's really we neat about these is an enhancement of being able to calculate exact values of certain special angles. We have the right to use these to prove identities and I want to begin with the cofunction identities for an example. Now you more than likely currently understand these identities but it's great to aid you remember them to be able to prove them utilizing the sine enhancement or subtractivity formulas, so the sine of pi over 2 minus theta. This is this is going to give us a cofunction identification, let's use the sine of a difference formula. It's sine cosine, sine pi over 2 cosine theta cosine sine, cosine pi over 2 sine theta bereason it's minus and sine sine says the very same, we have actually a minus. Now sine pi over 2 is 1 times cosine theta, cosine pi over 2 is 0, 0 times sine theta so this just becomes cosine theta and that's the formula we'll remember. Sine of pi over 2 minus theta equates to cosine theta.Likewise here's cosine pi over 2 minus theta, the cosine of a difference formula is what we need right here. The cosine of a difference formula goes cosine cosine sine sine. Cosine pi over 2 cosine theta sine pi over 2 sine theta and also cosine the sines adjust c for adjust so minus becomes plus.

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Remember cosine of pi over 2 0 sine of pi over 2 is 1 and also so we end up through sine theta. Cosine of pi over 2 minus theta equates to sine theta, so the cosine and sine enhancement formulas are really valuable for proving identities.