Answer the following questions without using a calculator.

CHEMISTRY · Multi-part · ISC · Chemistry · Alcohols, Phenols and Ethers · Aldehydes, Ketones and Carboxylic Acids

Problem

Answer the following questions without using a calculator. (i) Prove that arcsin⁡(35)<arccos⁡(35)\arcsin\left(\tfrac{3}{5}\right) < \arccos\left(\tfrac{3}{5}\right). (ii) Arrange the three numbers arcsin⁡(35)\arcsin\left(\tfrac{3}{5}\right), arccos⁡(45)\arccos\left(\tfrac{4}{5}\right) and arctan⁡(43)\arctan\left(\tfrac{4}{3}\right) in descending order, giving clear justification for each step of your reasoning.

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