Question

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Answer 1

Draw a Right Triangle. Pick an acute andgle and label it "x".

Using the information that cos(x) = 2/3, label the lengths of two sides.

Use the Pythagorean Theorem to calculate the value fo the 3rd side.

Think about what quadrant things are in and you are nearly done.

Answer 2

cos x = 2/3
1. Find cos x/2. Use identity: cos^2 x/2 = (1 + cos x)/2,
cos^2 x/2 = (1 + 2/3)/2 = 5/6 --> cos x/2 = sqr (5/6)...
2. Find tan x/2. Use identity: tan^2 x/2 = (1 - cos x)/(1+cos x)
tan^2 x/2 = (1 - 2/3)/(1 + 2/3) = 1/3 : 5/3 = ... --> tan x/2 ....
3. sin x/2 = tan x/2 *cos x/2 = ....

Answer 3

Keep in mind that 1/2 of angles in Quadrant IV are in Quadrant II.

Answer 4

Why are you not doing the work? There are known relationships between sine, cosine and tangent and the half-angles. Find them and use them. Let's see what you get.

Answer 5

Well, generally, two independent solutions resulting in the same conclusion usually is a pretty good sign. Unfortunately, you didn't actually show us any of your work, so there is no way for us to know if you are actually getting it.

Answer 6

Now we have three identical results?!

Part of what you should be doing is gaining your own confidence. Make your work clean, clear, and easy to follow. In this way, you will be able to SEE that you went through some process without error and you will gain confidence. Good work.

Answer 7

What was the answer for tan (x/2)? @queenbee232 @thu1935