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Expert: - 3/14/2011


Question

trig
i have tried to work with this problem in order to understand how to solve such problem but I get stuck at some point- looking for some one to explain things better than my tutor.

Answer
Questioner: vidhi
Country: United Kingdom
Category: Advanced Math
Subject: trigonometry
Question:

i have tried to work with this problem in order to understand how to solve such problem but I get stuck at some point- looking for some one to explain things better than my tutor.  
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Here is what you have:(t means theta)

sec t = sqrt(2), so cos t = 1/sqrt(2), which is Positive, which means t in Quad 1 or 4

Not only that, t has a reference angle of 45 deg, or pi/4.

So only  t = pi/4(Q1) or  t = - pi/4(Q4) are possible.

Comment:  7pi/4 is also in Q4, but you said you must have -pi < t < pi.

Now you need one more fact to decide: Q1 or Q4

cot t = -1, so tan t = -1.  This means t in Q2 or Q4.

Putting them together, t is in Q4 and t = -pi/4
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Paul Klarreich

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