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Sin Cosine and Tangent-Basic Trigonometry

3,749 views · Published 2 February 2016 · 5:41 · Indexed 27 October 2026

Channel: MooMooMath and Science · 2016 · Education

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In this video you the basics of sine, cosine, and tangent.

Transcript
Hi welcome to MooMooMath
Today we are going to look at Sin,Cosine, and Tangent
of angles, just the basic set up and what the ratios mean, and where the sides are.
I will call this first angle A 
Sin is equal to opposite side over 
We will take the cosine of angle D and the cosine is the adjacent over hypotenuse
Tangent will be the tangent of E which will equal the opposite over the adjacent side.
We will look at three different triangles and three different ratios and how to look at opposites and adjacent s.
We will figure out which sides are which.
What I always do is identify my hypotenuse first and label it.
I know the hypotenuse is opposite the right angle.
Now your adjacent and your opposite will change depending on your perspective.
If you are looking from A you have an opposite side and an adjacent side, but looking from B the opposite and adjacent sides will be different. It changes based on where you are.
What I always do, since I'm looking from A I mark the angle, and draw a line across the triangle.
This opposite side if often called little a because it is associated back to the angle A but this is the opposite side. I have now identified my opposite and hypotenuse so I can now set up a ratio. Now let's give them lengths.
Let's say the opposite side is 8 and the hypotenuse is 10 I can write the ratio as the sin of A = the length of 8 over length 10 which is the opposite over hypotenuse.
Now let's look at cosine of an angle.
We will take the cosine of D 
I have to change my perspective. I have to start at angle D 
I need to find adjacent over hypotenuse.
Let me go ahead and give each side a length.
This side is 3, this side is 4 and the hypotenuse is 5.
This is a right triangle because it is one of our triples.
I need to identify the adjacent side. 
To start, find the right triangle, and the hypotenuse will be opposite the  right triangle. 
Label it first.( opposite the right angle)
Now from angle D the side that measures 3 is my opposite side.
In cosine I don't need the opposite.
I will use the ratio of the other two sides.
This side is opposite, this side is hypotenuse, so the only one left over is the adjacent side. That makes sense because it is next to angle D So my adjacent over hypotenuse will be the ratio of these two sides so the cosine of D will equal 4 over 5
Now let's go down and look at a tangent
Tangent of E will be the ratio of opposite over adjacent
Tangent is the one trig function that does not have hypotenuse.
We will start from this angle, so mark the angle.
I will give you lengths of the sides 7,24, and 25
Those three sides form a right triangle
I will not use my hypotenuse and it is the easiest one to identify.
I will look opposite the right triangle so that is my hypotenuse
I will not use it so I will exit it out
Now from angle E I will draw across, and that is my opposite side 
24 is my only other side and that is my adjacent, and yes it does help form the angle, one of the sides of E, so my ratio will be Tangent of E is equal to 7 over 24, and that is how you set that tangent up, and how you find opposite over adjacent, and hypotenuse for each triangle.
Hope this video was helpful.

You may also enjoy...
Basic Trig Sin Cosine Tangent
https://www.youtube.com/watch?v=X5uFqpypDy4

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