Pre-Calculus Help Please.?

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Mike

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Give exact answers for 0 less than or equal to theta is less than or equal to pi/2

If cos theta= 1/2, what is sec theta? tan theta?

If cos theta= 1/2, what is csc theta? cot theta?

If sin theta = 1/3, what is sec theta? tan theta?

How do I do these problems? Please show work. I have been on these problems for hours. Please Help. Thank You!
How do you get those answers for question one?
 
Remember cosine = adjacent/hypotenuse, sine = opposite/hypotenuse, tangent = opposite/adjacent or sine/cosine, secant = 1/cosine = hypotenuse/adjacent, cosecant = 1/sine = hypotenuse/opposite, and cotangent = 1/tan = adjacent/opposite or cosine/sine. Use the Pythagorean theorem a^2 + b^2 = c^2, where a and b are the legs and c is the hypotenuse. Draw right triangles for each problem and label an angle as θ to help you.

1.) cosθ = 1/2, which means the adjacent side is 1 and the hypotenuse is 2. Secant is hypotenuse/adjacent, so secθ = 2/1 or just 2. Now you have to find the side opposite the angle in order to find the tangent. You can use the Pythagorean theorem to find it, which would be √(2^2 - 1^2) = √3, which means tanθ = √(3)/1 or just √3.
secθ = 2, tanθ = √3

2.) cosθ = 1/2, which makes the adjacent side 1, the hypotenuse 2, and the opposite side √3 like in the first problem. Therefore, cscθ = 2/√(3) or 2√(3)/3 when rationalized, and cotθ = 1/√(3) or √(3)/3 when rationalized.
cscθ = 2√(3)/3, cotθ = √(3)/3

3.) sinθ = 1/3, so the opposite side is 1, the hypotenuse is 3, and the adjacent side is √(3^2 - 1^2) = √8 = 2√2. Therefore, secθ = 3/(2√(2)) or 3√(2)/4 when rationalized, and tanθ = 1/(2√2) or √(2)/4 when rationalized.
secθ = 3√(2)/4, tanθ = √(2)/4
 
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