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Unformatted text preview: ometric functions, however, we are now in a position to solve these equations. A good parallel
to keep in mind is how the square root function can be used to solve certain quadratic equations.
The equation x2 = 4 is a lot like sin(θ) = 2 in that it has friendly, ‘common value’ answers x = ±2.
The equation x2 = 7, on the other hand, is a lot like sin(θ) = 1 . We know8 there are answers, but
we can’t express them using ‘friendly’ numbers.9 To solve x2 = 7, we make use of the square root
7 Or, alternatively, setting the calculator to ‘degree’ mode.
How do we know this again?
This is all, of course, a matter of opinion. For the record, the authors ﬁnd ± 7 just as ‘nice’ as ±2.
8 10.6 The Inverse Trigonometric Functions 717 √
function and write x = ± 7. We can certainly approximate these answers using a calculator, but
as far as exact answers go, we leave them as x = ± 7.10 In the same way, we will use the arcsine
function to solve sin(θ) = 1 , as seen in the following example.
Example 10.6.7. Solve the following equations.
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