Basic Trigonometry: Sin Cos Tan (NancyPi)

MIT grad shows how to find sin, cos, and tan using SohCahToa as well as the csc, sec, and cot trig functions. To skip ahead: 1) For how to find the adjacent, opposite, and hypotenuse sides of the right triangle, skip to 1:13. 2) For how to find the value of SIN of theta using SOH CAH TOA, skip to 3:16. 3) For how to find COS, skip to 4:15. 4) For how to find TAN, skip to 4:56. 5) For how to find CSC, SEC, AND COT from the sin, cos, and tan functions, skip to 5:56. 6) For harder examples of how to label the adj, opp, and hyp sides if the TRIANGLE IS ROTATED on its side or upside down, skip to 8:32. Nancy formerly of MathBFF explains trigonometry basics.

SIN COS TAN: If you have a right triangle with side lengths given and an angle (theta), you can easily find the sine, cosine, and tangent trigonometric functions. Remember that the longest side of the triangle is the 'HYPOTENUSE', the side directly opposite theta is the 'OPPOSITE', and the other side next to theta is the 'ADJACENT' side.

Once you've identified the hypotenuse (H), adjacent (A), and opposite sides (O), you can find Sin, Cos, and Tan using these trigonometric ratios:

Sin of theta = Opposite over Hypotenuse (SOH)
Cos of theta = Adjacent over Hypotenuse (CAH)
Tan of theta = Opposite over Adjacent (TOA)

The mnemonic SOH CAH TOA can help you remember which sides to use for the sine, cosine, and tangent trig ratios. For instance, SOH stands for Sin = Opposite over Hypotenuse

CSC SEC COT: If you need to find one of the other three trig functions (cosecant, secant, or cotangent), the easiest way to find them is to first find Sin, Cos, or Tan and then take the reciprocal (or flip) the fraction, since:

Csc = 1 / Sin
Sec = 1 / Cos
Cot = 1 / Tan

For example, if you find that Cos of an angle is equal to 3/5, the Sec of that angle would be equal to 5/3.

[teev]

I like the fact that you take your time; it gives me time to process what I'm learning.

[archiem]

Forcing myself to learn this 20mins before my exam

[nicolehicks]

This is so useful during quarantine. My teacher stopped teaching and its just book work so you're so helpful thanks.

[edhead]

Your ability to write backwards so easily blows my mind. Thank you for the clear explanation. I keep this video at bay as it is the best explanation I've come across.

[ToadSprockett]

Thank you for making this so simple and clear, I barely made it out of college algebra and now find that I need a solid base of trig for development. You definitely have the gift of teaching, again thank you for sharing...

[paulbull]

45 years old and finally someone made sense of this for me. Thank you.

[siennablack]

I love how you take things at a steady pace, and explain it thoroughly. It really helps me learn. Also!! The setup is so pleasing and easy to learn from :)

[OpticalMessiah]

Thank you for the review. Haven't seen much trigonometry since I retired as an optometry professor 12 years ago.
Very good effort and easy to understand.

[ReplicaThirty]

If anyone is wondering what the functions actually are, rather than just how to to calculate them, they're ratios. For example, 5/10 = 0.5 is essentially saying that 5 makes up 50% of 10. Likewise, for SIN as an example, it's basically saying the Opposite makes up result% of the Hypotenuse. In her example of sin, Nancy has it equal to 4/5. This means that the length of the opposite makes up 80% of the length of the Hypotenuse. This of course applies for all the trig functions.


If you want to know what they're used for, Nancy did another awesome video explaining it here:

[progresspiper]

31 years ago, I spent a whole school term trying to understand this. I never could. Now, after 13 minutes, I do.

[jay-peephillips]

So calmly expressed with a soft teaching voice that enables one to grasp. Thanx and much appreciated Nancy!

[abbeylo]

This really really helped me understand it! Thanks so much! Your pace at which you go is perfect because it allows me to take my time in understanding the material.

[spurii]

Brilliant! Very easy to follow - Clear and Precise speech - Nice steady pace - perfect simplicity - I have confidence in this subject in less than 15 minutes - THANKS Nancy XX

[apricity]

I just realized, she's writing this entire thing backwards.

[geraldbrooks]

Thank you so much!! I barely got through algebra in college and have only used basic arithmetic since then. Now that I'm retired, I am determined to learn the fundamentals of trigonometry so I can finally understand how, after "shooting the stars" with a sextant, accurate timepiece, and various navigational publications, my fellow quartermasters and I were able to find our ship's position on the high seas. I appreciate your calm, unhurried teaching style and will be watching all of your videos. Thanks again!!

[peacemac]

This helped so much during this "online only" coursework I'm doing rn. Thank you :)

[dennislaux]

I LOVE learning with this woman. She makes it easy and I can focus on the problem. Really wonderful teaching skills.

[trippledove]

This was the first time ever that I was able to grasp what was going on! You are awesome!

[basstherapyasmr]

Amazing explanation. I saw this crop up in a programming example. It was an animation of the Earth circling the Sun. In the code it used sin and cos to determine where to draw the Earth. I didn't know anything about it so I searched and found your video. Really cleared it up for me. Thanks!

[shastrophile]

Thank you so much! I missed the lesson in class, but thank god i have found your channel!this is the first time that i understand a math lesson without asking a teacher..appreciated!💜