Trigonometric identities / equations worksheet

joeyfpurdy

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Feb 16, 2014
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1.) If cos θ = 2/3, what is tan θ? Show work.

2.) If sin θ = 1/2 and θ is in quadrant I, find in 2 θ. Show work.

3.) Prove cos(α - β) = cos α cos β + sin α sin β. Show work.

4.) Solve 2cos^2x - 3cosx + 1 = 0 for 0 ≤ x < 2 π. Show work.

5.) Solve 2sinx - 1 = 0 for 0° ≤ x < 360 °. Show work.

6.) Solve sin^2x = cos^2x for 0°≤ x < 360 °. Show work.

7.) Solve: sinx - 2sin x cos x = 0 for 0 ≤ x < 2 π. Show work.

Any help is appreciated, thank you for you time.
 
1.) If cos θ = 2/3, what is tan θ? Show work.

Any help is appreciated, thank you for you time.
I'm afraid you have the wrong idea: we do not give answers; instead, we help YOU do the work. After all, we will not be there when you take your test.

Start by reading READ BEFORE POSTING.

One of the things that you will see there is that we do not like a list of problems: the guideline is one problem per thread. Let's deal with problem 1. You can post the others in separate threads after you read READ BEFORE POSTING.

Is the tangent defined in terms of other trigonometric functions? What is perhaps the most common of those definitions? How is that helpful?

One of the fundamental trig identities allows you to find the sine of an angle if you know the cosine or to find the cosine if you know the sine. You need to memorize that identity because it comes up again and again. What is that identity?
 
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