Pre-Calc Project
نص القصة المصورة
- I'm struggling in my Pre-Calc class so much. I just wish there was someone that could help me.
- Do not worry young man... I am Calculus Man.
- RadiansA radian is an angle in which a corresponding arc in a circle is equal to the radius of the circle. It is important to remember this rule when using radians.2π radians= 360 degrees so...π radians = 180 degreesTo convert from degrees to radians, multiply the degree by 180/π.
- Woah where are we?
- Time to learn my friend. First lesson is radians. Read the board.
- The Unit CircleThe unit circle is a circle of unit radius in which the radius is 1 throughout the circle. Remember:x,y = cos,sinπ/3 = 1/2,sqrt{3}/2π/4 = sqrt{2}/2,sqrt{2}/2π/6 = sqrt{3}/2,1/2There are four quadrants. To know where numbers are positive, remember the acronym ASTC (all students take calc): Quadrant I (all are positive), Quadrant II (sin positive), Quadrant III (tan positive), and Quadrant IV (cos positive).
- Interesting. What's next?
- The unit circle is quite interesting. Take a look.
- QSFRWhen an angle moves into quadrants, we have to know the sign of thefunction value. Using reference angles can help to find the exact value. The acronym QSFR is useful for these type of problems. Be sure to find:Q = QuadrantS = SignF = FunctionR = Reference Angle
- QSFR what?
- Introducing QSFR.
- Inverse Trig EquationsInverse trig equations are the inverse functions of the basic trig function. First, find the reference angle. Then, determine what quadrant the function is positive or negative depending on the question. Finally, determine the angle.The inverses of a function can be written as sin^-1(O/H) = angle; cos^-1(A/H) = angle; tan^-1(O/A) = angle. For example, tan (angle) = -1 can be rewritten as tan^-1(-1) = angle.
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