Trig Relationship cosine of arcsine?

There is no way to simplify... It is possible when it is a function and the inverse function...

For example...a) ln e^7 = 7 , b) cos(arccos10) = 10 , c) arcsin(sinx) = x .... d) sqrt( 5^2) = 5

But here cos(arcsinx) it is not a function and the inverse... then we cannot simplify. OK!

permit's look on the definitions of Sine, Cosine and Tangent. First, we'd desire to label the three factors of a righ triangle. permit's think of roughly being on the vertex of one of the angles that's not the ninety degree perspective. There are 3 factors. there is the different (call this length O), there is the single which is longer than the different 2 factors (the Hypoteneuse -- call its length H) and the different one -- which we are able to call the adjoining area -- with length A. the way I bear in suggestions this is SOH-CAH-TOA -- which replaced into the call of a fave Indian. yet i replaced into in severe college whilst snicker-IN replaced into on, and the capture word on that teach replaced into "sock-it-to-me" which jogs my memory of SOHCAHTOA SOH -- Sine = opposite over hypoteneuse --> S = O/H This tells us why Sine is often under one -- because of the fact H is the longest area, so the ratio should be under one. CAH -- Cosine = adjoining over hypoteneuse --> C = A/H This tells us why Cosine is often under one -- because of the fact H is the longest area, so the ratio should be under one. TOA -- Tangent = opposite over adjoining --> T = O/A right here, we don't understand that's larger -- O or A, so this might handle any fee above 0. Now -- what happens if the attitude is particularly small -- then the different area would be small in assessment to the adjoining area -- so the ratio would be close to to 0. What happens whilst the adjoining area is small? the different area gets larger. yet it won't be able to get larger than the hypoteneuse. the attitude won't be able to be greater desirable than ninety levels -- considering you have already got one ninety degree perspective & the different 2 might desire to function as much as ninety (considering all 3 upload as much as a hundred and eighty). because of the fact the adjoining area gets smaller & smaller, the tangent will might desire to get larger & larger.