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Basic Trigonometry and an Application
Transcript of Basic Trigonometry and an Application
sin theta = y/1, cos theta = x/1
and tan theta = y/x We can think of tangent as the rise over the run for the angle we are looking at.
It's the opposite side (the rise) divided by the adjacent side (the run). What if the hypotenuse isn't conveniently 1 unit long? Then what? We will just use the length of our hypotenuse instead of using 1. We can come back to SOH CAH TOA to help us remember the formulas. I sure hope that kid's toe doesn't get infected! ;-P Hey! Wait a minute! The sine and cosine just have 1's on the bottom. Does that mean that for a unit circle, x = cos theta and y = sin theta? And the tangent formula kinda reminds me of the slope formula! Great connection! SOH: sin theta = opposite/hypotenuse CAH: cos theta = adjacent/hypotenuse TOA: tan theta = opposite/adjacent How is this going to help me with physics? If we are given the total velocity of a projectile (for example) and know its launch angle (theta), we can figure out it's x and y components using trig. sin theta = y velocity/total velocity
we can use to solve for y velocity:
y velocity = total velocity * sin theta cos theta = x velocity/total velocity we can use to solve for x velocity:
x velocity = total velocity * cos theta Ok. I think it makes sense! If I have any questions though I will be sure to ask! Projectile Motion Analyzing our projectile's motion