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    how would you work out these without a calculator
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    Look through examples 15-17. They show you that arcsin lies within the interval of -π/2 ≤(alpha)≤π/2 and gives you the intervals of arccos and arctan.

    For question 1.a) of 6E: arccos0 can be found easily by looking at the graph which you can find on page 99. At x=0 , π/2 is the corresponding value on the graph.
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    (Original post by JSM1)
    how would you work out these without a calculator
    Use these common values of sin, cos and tan. You should try to learn them. These are how I remember them (some textbooks write them differently):

    sin 0 = 0
    sin π/6 = 1/2
    sin π/4 = (√2)/2
    sin π/3 = (√3)/2
    sin π/2 = 1

    cos 0 = 1
    cos π/6 = (√3)/2
    cos π/4 = (√2)/2
    cos π/3 = 1/2
    cos π/2 = 0

    tan 0 = 1
    tan π/6 = (√3)/3 (also commonly written as 1/√3)
    tan π/4 = 1
    tan π/3 = √3
    tan π/2 = [undefined]

    Also, don't forget the trig identities (for example, sin(180 - x) = sin x).
 
 
 
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