Pre-Calculus Quiz Review. Hosted by: Dr. Bruce Piper and TLA Bharath Krishnamurthy. Advising and Learning Assistance Center. Located at Russell Sage Lab 1st Floor Provides Academic Advising Offers great tutoring services to all students alac . rpi . edu . Overview. Exponents
Pre-Calculus Quiz Review Hosted by: Dr. Bruce Piper and TLA Bharath Krishnamurthy
Advising and Learning Assistance Center • Located at Russell Sage Lab 1st Floor • Provides Academic Advising • Offers great tutoring services to all students • alac . rpi . edu
Overview • Exponents • Logarithms • Unit Circle/Trig Functions
Exponents Exponent Base
Simple Exponent Rules to Remember! Remember these rules only apply to LIKE BASES
Logarithms bc = a logba = c Logarithmic functions are inverses of exponential
Simple Logarithm Rules to Remember: Pay attention to LIKE bases!!!!
Couple of Side Notes ‘ln’ is “natural log” which is the SAME thing as logex. ‘e’ is a constant with a value 2.718. It has special meaning because the slope of a tangent line of a function of ‘e’ is the function itself. (Dont worry if you don’t understand this bit) DON’T GET CONFUSED BY THE TERM ‘ln’. It just means log base ‘e’. You don’t need to memorize the value of ‘e’. You can just express your answer in terms of ‘e’!!
Unit Circle • Circle of Radius 1 • Constructed from pythagoream’s theorem • Angles correspond to points along the circle: these define our values for cosine and sine
Trigonometric Functions • From the unit circle we can deduce: • sin(x) = y/r • cos(x) = x/r • tan(x) = y/x • …and of course we all know that x2 + y2 = r2
Example Problems with Right Triangle: Given that cos (θ) = − 3/ 4 and that sin (θ) > 0, ﬁnd tan (θ) and express your answer in simpliﬁed form (without trigonometric functions). For some real number x, it is known that sin(x) = ¼ and cos(x) > 0. The value of cos(x) can be written as √α / 4. What is α?
Common Trig Values to Memorize: Note how sin is ascending and cos is descending If you have these down, then the tan is simple sin/cos! Add npi to go to different quadrants on the coordinate axes All Students (sin is positive in 2nd) Take (tan is positive in 3rd) Calculus (cos is positive in 4th)
Inverse Trig Functions The expression sin(x) = ½ reads “the sine of x is one half”. The expression sin-1(1/2) = ? is the opposite of the above expression. It can also be interpreted as: “The sine of some angle is ½, what is the angle?”
Example Problem Evaluate: tan(sin-1(1/√2)) tan(cot-1(1/3))