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This Lesson (Using 30,60,90 Triangles and ASTC to solve trig equations) was created by by swincher4391(1107)
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Consider a 30,60,90 triangle.
We know from converting radians and degrees, that these triangles are equivalent. Here is it in radian form: 
This second triangle is how the ================================ Now consider a 45,45,90 triangle. 
Its radian counterpart is: 
This is how the ==================================== Now just remember SOH-CAH-TOA, sin = opp/hypo cos = adj/hypo and tangent = opp/adj, and you should be able to find any of these values using the triangles. ==================================== Remember (x,y) = Consider the quadrangles from [ 
Then by looking at the points, we can figure out easily what the values are at those angles. So we have the fundamental angles and their values... how do we extend it to We need to know two things. The reference angle and the starting angle. Step 1) Find what quadrant the angle you are given is. Step 2) Starting with your angle find the nearest angle that lies on the x-axis. These are the multiples of pi (0,pi,2pi,3pi) etc... Step 3) Going counterclockwise, if the angle is behind you, take your starting angle and subtract your x-axis angle. If it is in front of you, take the x-axis angle and subtract from it the starting angle. (Note 0 = 2PI) This new angle is your reference angle. It should between 0 and Step 4) Use this as your new value to find the sin, cos, tan.. etc of. Step 5) Determine whether your value should be positive or negative. Use the chart below to determine. *** Note : A- All positive, S- sin positive, T- tangent (which implies sin and cos are negative), C- cosine *** 
That's it! Let's go through an example. Step 1)What quadrant is Step 2) The closest angle would be in front of me at Step 3) So I take Step 4) Look at the triangle to see that Step 5) Reference ASTC. In Q4 we have a C. This means cosine is positive, sine is negative. We have sin, so our answer is negative. The answer then is Let's ask the opposite question now. Go in the exact opposite order. One might be inclined to say that the answer is Look at our triangle. At which angle is So we ask this question, in what quadrants is sin negative? We look and we see that in Q3 and Q4 sin is negative. Locate the x-axis angle in Q3 first: it is So what is Locate the x-axis angle in Q4: it is So what is So our answers are I hope this helped! This lesson has been accessed 12194 times. |
