Review Midterm 3 •
You will have 50 minutes to take the exam in class on November 22nd. •
You will be allowed to use 3x5 index card with hand written notes on both sides. Make sure it is truly a 3x5 index card and not something that closely resembles a 3x5 index card. •
You will NOT be allowed to use a calculator (or other electronics), notes, textbook, or your neighbor. •
You must show your work to receive credit. (You work should be organized and legible.) •
Scratch paper will be provided; scratch work will not be graded. •
Bring your student ID and a pencil. •
The midterm will cover Chapter 5 and Chapter 6. You should be able to… Convert between radian and degree angle measures. Find the reference angle of a given angle. Find coterminal angles of a given angle. State the arc length formula and understand how to use it. Understand and use the unit circle, general circle, and right triangle definitions of trigonometric functions. • Explain the relationship between the distance formula and the definition of a circle. • State the standard form of the equation of the unit circle. • State the standard form of the equation for a general circle centered at the origin and identify the radius •
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π
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π
4
• Evaluate trigonometric functions of basic angles (multiples of 0, , and ) exactly. • Construct the unit circle. • Identify the sign of each of the trigonometric function in €each quadrant. €
• Analyze trigonometric functions o Identify Domain o Period o Amplitude o Transformations o Identify x-­‐intercepts & y-­‐intercepts o Identify asymptotes • Graph the functions and transformation of trigonometric functions. • State the domain and range of the inverse trigonometric functions. • Graph the inverse trigonometric functions. • Solve right-­‐triangle problems. • State the law of cosines and understand how to use it. • Understand the relationship between the Pythagorean theorem and the law of cosines. • State the law of sines and understand how to use it. • Identify whether given information about a triangle results in 0, 1, 2 or infinitely many triangles. • Solve oblique triangle problems. • Find the area of a triangle. • Use identities to rewrite trigonometric expressions. • Use definitions of the inverse trigonometric functions to rewrite trigonometric expressions. • Use definitions of inverse trigonometric functions and reference triangles to rewrite expressions. • Use identities to evaluate trigonometric expressions exactly. • Use definitions of the inverse trigonometric functions and reference triangles to evaluate trigonometric expressions exactly. • Prove Trigonometric Identities • Solve Trigonometric Equations (Find principle-­‐value, restricted, and complete solutions.) • Convert between rectangular and trigonometric form of complex numbers. • Multiply and Divide Complex numbers. • State DeMoivre’s theorem and use it to find all positive integer powers of a complex number. • State nth root theorem and use it to find all roots of a complex number. Practice Problems: Ch. 5: p. 369-­‐370 (Self-­‐Test) #1, 2, 4-­‐8 all p. 370-­‐371 (Practice for Calculus) #17-­‐26 all, 37-­‐43 all Ch. 6: p. 421 (Self-­‐Test) #1-­‐10 all p. 422-­‐423 (Practice for Calculus) #1-­‐4 all, 13-­‐16 all, 21, 22