Trigonometric Ratios For Any Angle - Quadrant by Quadrant

Watch this video to learn how you can determine the primary trigonometric ratios for any angle, especially those that are over 90 degrees.

[@nishchaysingh__9b__265]

Great explanation!! Really loved it.

[@Fancywheels]

Was really helful! Thankyou

[@fredkong6671]

You’re welcome. Glad it helped!

[@FaheeemKhan-tt3ww]

Great 👍

[@fredkong6671]

Thank you! Cheers!

[@ebenezergyimah507]

please , what's the name of the software you used as your black board?

[@fredkong6671]

Hi Ebenezer, thanks for checking out my math videos. I use SMART Notebook software with this storyboarding technique. I set the background to black, then use the tools to create multiple slides where each one is just slightly different than the one before. If you don't have SMART Notebook, you can probably get a trial version online from SMART Technologies.

[@ebenezergyimah507]

@@fredkong6671 Thanks so much Fred, I will get in touch often

[@abdullahtauhid1908]

I have only one doubt. If the angle is outside of the Triangle, then how are you measuring It's ratios? It does not have any side, cause It's not inside a triangle. So how are you measuring the ratios, if there are no Opposite or Adjacent side of that angle?

[@fredkong6671]

Good question, Abdullah! I admit it is not clear in the video, but what I am doing here is using the reference angle. For example, at 2:21, I refer to the angle theta as 100°. It's true that 100° is an angle outside of the triangle, so it would not have an opposite or adjacent side. However, if you use the corresponding reference angle (the acute angle between the terminal arm of the rotation angle and the x-axis), or 80°, or the measure of the angle that IS inside the triangle, then you do have the opposite and adjacent sides. It turns out that that is how we can think of the sine, cosine, or tangent ratios of 100°, namely that they are precisely the ratios of the triangle with the corresponding reference angle. You just have to make sure to take into account which quadrant you are in, because the quadrant will dictate whether the opposite and adjacent sides are negative or positive. Phew! That was a mouthful, but hopefully this helps!

[@abdullahtauhid1908]

@@fredkong6671 So an angle's ratios would be the ratios of a triangle that has It's corresponding reference angle?

[@fredkong6671]

That is correct. Just make sure you also consider whether the ratio should be positive or negative depending on which quadrant you find the terminal arm.

[@Shefa-lt6lf]

Theta angle is outside of the triangle in 2nd,3rd,4th quadrant.....😮