Pre-Calculus Quiz Review Hosted by: Dr. Bruce Piper and TLA Bharath Krishnamurthy

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Overview Exponents Logarithms Unit Circle/Trig Functions

Exponents Base Exponent

Simple Exponent Rules to Remember! Remember these rules only apply to LIKE BASES

Examples:

Logarithms log b a = c b c = a 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 log e x. ‘e’ is a constant with a value 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’!!

Example Problem:

Problems for you to try:

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 x 2 + y 2 = r 2

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 4 th )

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))