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Know your strong points and your weakness. Are you good at memorizing? Are you a quick learner? Do you understand better while doing exercises or listening an explanation?
Use your strengths and work them out to improve.

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we all know how different we are from one another, do not try to do the things that work on the majority and start doing the things that work on yourself. You do not have to use the most common method but the most efficient of them. You can change your methods between subjects, it is definitely not the same to study math as to study chemistry nor biology nor history. Take your time to define the method that works for you, it will save you time in the long term.

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Even though the words are important, the information is mostly gathered on the question, read the question first and then search for the numbers you need to solve the problem.

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Most of the time you face a long problem you waste your time. At first, while thinking how long it is, and then you lose focus and by consequence do not understand what is really being asked. Do not panic and focus on the "what are they asking" instead of "how long and complicated is the question".

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If you understand the first quadrant and associate the coordinates and signs you just have to apply your knowledge and forget about memorizing.

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As students everybody knows time has a lot more value than money, but most of the times you memorize things to "optimize time" you have to exponentially increase the time you saved when the topic is already forgotten. Memorizing its faster but understanding last longer.

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If we pay attention we notice a pattern on the shape and measurements of the quadrants, that being said we find the sine and cosine as similar and repetitive places on coordinates.

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We can use symmetry to find out and fill the sine and cosine values of the unit circle by understanding their relationship with the x-axis and y-axis and the coordinates. Including the positive and negative values of the x-axis and y-axis

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we can observe how the reference angle is 45, hence, the cosine and sine absolute value will not vary.

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The sign of the value of the sine and cosine will depend of the quadrant where the original angle was.

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The absolute values of the cosine and sine of the starting angle will be the same as the ones of the reference angle.

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It is the smallest angle that can be made by the terminal side of a given angle and the x axis

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Since the x coordinate has a limit of [-1,1] the range of the sine and cosine functions is bounded by it and is the same: [-1,1]

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The input to the sine and cosine can be any real number.

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the smallest and largest number that can be an output of the function.

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The smallest and largest number that can be input of the function.

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when we obtain this measurements we know the first quadrant of the unit circle.

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We double the triangle to get an equilateral triangle; from there we can get the cosine knowing the radius is 1 and the sine is 1/2

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45° are equivalent to π/2.
A triangle with 45° is isosceles, hence, the x and y coordinates are the same, and so are the sin and cosine.

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Since the Pythagorean theorem says "a^2+b^2=h^2"
And in the unit circle hypothenuse (radius) =1, a (y)= sin, and b (x)= cos we are left with

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They are easy to recognize since:
x= cosine
y= sine

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A circle centered at the origin with radius 1

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Domain and Range of sin and cos Functions

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Domain and Range of sin and cos Functions

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Function Values for the sin and cos of special angles.

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Function Values for the sin and cos of special angles.