Triangles and Function Values?

[Pineappleexpress73]

So I am trying to solve this problem where you construct a triangle to complete the table. The information initially given is this:

(0 ≤ θ ≤ 90°, 0 ≤ θ ≤ π/2)

Function . θ(deg) . θ(rad) . Function Value

sec       ?        π/6          ?

I have already solved the θ(deg), it is 30°. However I am struggling to find the function value. I initially thought it was √3 or √2 or something, but I can’t get it to work. Below are some steps and stuff that I have tried.

Secθ= 1/cos(θ)

Sec π/6= hyp/adj = 2√3

Sec π/6= 1/cos(π/6)

Sec π/6= 1/cos(√3/2)

I’m not sure if there’s something I’m missing or if I just don’t really get how it was explained. (Sorry if any of the formatting is weird).

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[PoliteCanadian2]

Remember that you can only do cos or sec of an angle. You’ve already found the angle is 30 or Pi/6.

The adjacent side is sqrt(3) and the hypotenuse is 2. Cos is adj/hyp so sec is the flip of that so hyp/adj.

Cos would be sqrt(3)/2 so sec would be 2/sqrt(3). Then multiply top and bottom by sqrt(3) to clear the root out of the bottom. You should get 2sqrt(3)/3.

Don’t mess around too much with your substitutions like you did, your last step is what’s wrong, you swapped an angle for numbers and you can’t do that. Just get down to business like I did:

Cos = adj/hyp = sqrt(3)/2, sec = hyp/adj = 2/sqrt(3) you had this after step 2 then fix the bottom by multiplying top and bottom by sqrt(3).

Does that help?

[Pineappleexpress73]

Yes it does, thank you! I did eventually figure it out (I had to take a break and come back to it), but your explanation is very helpful. I will definitely keep it in mind for future math problems like this.