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# Right-triangle relationships: Draw a right | Ch 1 - 45RE ISBN: 9780321570567 2

## Solution for problem 45RE Chapter 1

Calculus: Early Transcendentals | 1st Edition

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Problem 45RE

Right-triangle relationships: ?Draw a right triangle to simplify the given expression Ass?ume x> 0 ?and 0?????/2. cos (2 ?sin?1 ?x? ?(Hint: Use ? os 2??= ? os2 ?? sin2 ? .)

Step-by-Step Solution:

Step-by-step solution Step 1 We need to draw a right t1angle and use right triangle relationships to simplify the expression cos (2sin (x)) assuming x > 0 and 0 . 2 Step 2 To simplify the expression, we first draw a right triangle with an angle , such that: = sin (x)  sin = x  We know from right triangle relationships that: sin = opp hyp Since: sin = x = 1 We now know that: opp = x, hyp = 1 The resulting right triangle is shown below:

Step 3 of 3

##### ISBN: 9780321570567

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