What should I study to know how to solve?

I'm studying for a test, and they have several questions I've never dealt with, and I don't even know what the topics I should study are. Here are some of them:

cos δ = 1, which of the following could NOT be a value of δ?

Which of the following is equivalent to 2sin2θ+(1–cos2θ)/(tan2θ)?

If sin∂=sqrt32, what is the value of cot∂?

All that I want to know is WHAT I SHOULD STUDY to know how to solve these type of questions, since I have no idea how to even tackle them. I don't actually need the answers, just the names of the methods. Thanks!

1 Answer
Apr 9, 2018

For the first question, know your unit circle and special angles. Here is an image:

https://www.mathsisfun.com/geometry/unit-circle.htmlhttps://www.mathsisfun.com/geometry/unit-circle.html

So if costheta = 1, then theta = 0. Thus theta != pi/2, (3pi)/2, pi/6, ..., many answers possible.

For the second, you need to know your trig identities. Here is a picture of those that I think are most necessary to learn.

http://carbon.materialwitness.co/trig-identities/http://carbon.materialwitness.co/trig-identities/

We can simplify as

2(2sinthetacostheta) + (1 -(1 - 2sin^2theta))/((tan theta + tan theta)/(1 - tanthetatantheta)

4sinthetacostheta + ((2sin^2theta)(1 -tan^2theta))/(2tantheta)

4sinthetacostheta + (2sin^2theta - 2sin^2thetatan^2theta)/(2tantheta)

4sinthetacostheta+ sin thetacostheta- sin^2thetatantheta

5sinthetacostheta - sin^3theta/costheta

A lot of expressions cancel to things like secx or tan(2x) which is always really nice.

As for the last problem, this example is implausible as -1 ≤ sin alpha ≤ 1 and sqrt(32) > 1. So I will use sinalpha = 1/sqrt(32). Since cscalpha = 1/sinalpha, we can see that cscalpha = sqrt(32).

Now from above you can see that 1 + cot^2x = csc^2x.

1 +cot^2alpha = 32

cot^2alpha = 31

cotalpha= +-sqrt(31)

If they clarify that alpha is in quadrant 1 we can guarantee that it will be positive. Similarly if alpha is in quadrant 2 then it will be negative. But when unspecified, keep the +-.

Hopefully this helps, please ask if you have any further questions!