A List of Problems it is Inexcusable Not to Know How to Solve! (Post-Notes 12 Edition version 0.02) 1. Find the distance traveled about the equator of a spherical planet with radius 30 km, by an object that travels from a city having longitude 12°32' to a city having longitude 23°14 ' . 2. Given that α is an angle in standard position that terminates in QIII, and that tan (α ) = 15 , find the approximate value of csc (α ) correct to three decimal places using only your calculator (no writing! other than the answer…). 3. Given that cos ( 73.2° ) = 0.853 , which it doesn’t, find the correct (for this problem), values of all six trig functions evaluated at 196.8° . 4. State the principal coterminal angle and a generalization of all angles coterminal to 954π . 35

⎛ ⎛ 19π ⎞ ⎞ ⎛ ⎛ 73π ⎞ ⎞ 5. Evaluate sin −1 ⎜ sin ⎜ and cos −1 ⎜ cos ⎜ . ⎟ ⎟ ⎝ 20 ⎟⎠ ⎟⎠ ⎝ ⎝ 17 ⎠ ⎠ ⎝ 6. Given that cot ( A ) = −

9 and A ∈QII , find sec ( A ) . 16

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7. Find a and b so that y = 4 tan a 2 x − b + 2 has a period of 16 and a “starting point” of 9.

⎛π ⎞ 8. State the period and amplitude of the function g ( x ) = 5 − 9sin ⎜ ( x + 3)⎟ . ⎝ 18 ⎠ 9. State all asymptotes using the general form x = a + b ⋅ n , with a being the first positive value at which f ( x ) has an asymptote, and the domain of the function

⎛x ⎞ f ( x ) = −3 + 7sec ⎜ + 9π ⎟ . ⎝5 ⎠ 10. A sinusoid passes through the points in the table 3 9 15 21 27 x y -5 2 -5 2 -5 Write positive and negative sine and cosine functions passing through the points. Graph your functions to confirm they work.

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⎛ 3 3⎞ 11. Evaluate sin −1 ⎜ − and solve sin ( x ) = − . What’s the difference? ⎟ 2 ⎝ 2 ⎠ ⎛ ⎛ ⎛ ⎛ ⎛ ⎛ 4⎞⎞⎞⎞⎞⎞ 12. Evaluate sin ⎜ tan −1 ⎜ cos ⎜ sin −1 ⎜ cot ⎜ sin −1 ⎜ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ . ⎝ 5⎠⎠⎠⎠⎠⎠ ⎝ ⎝ ⎝ ⎝ ⎝

13. State the domain and range of the three inverse trig functions we studied. 14. Solve the equation sin ( 3x ) + cos ( 2x ) − tan ( 4x ) = 6 on the interval 12 ≤ x ≤ 14 using your calculator. Obviously you need three decimals in your answers. 15. Solve the equation 6sin ( 2x ) sin ( 5x ) + 2sin ( 5x ) = 3sin ( 2x ) + 1 for all x by hand. 16. State the 14 Formulas! 17. Evaluate sin ( A − B ) , given that cos ( A ) =

3 with A in QIV and B = 3A . 5

18. Evaluate cos ( a ) sin ( b ) given that sin ( a + b ) = m and sin ( a − b ) = n . 19. Find the amplitude of the function y = 12sin ( 3x ) − 5 cos ( 3x ) .

2 ⎛ 3π ⎞ ⎛ 3π ⎞ 20. Solve cos ( 5x ) cos ⎜ ⎟ + sin ( 5x ) sin ⎜ ⎟ = − for all x. ⎝ 7 ⎠ ⎝ 7 ⎠ 2 21. Graph the function y = 8 − 2sin 2 ( 4x ) by hand. 22. Solve the triangle ABC with C = 54° , a = 43 , and c = 35 . 23. Find the area of the triangle CVS with c = 24 , s = 15 , and V = 134° . 24. Without a calculator find the sine of the angle between the vectors 2,5 and −3, 4 . 25. Without a calculator find the area of the triangle spanned by 4i + 6 j and 5i + 8 j . 26. The vectors a and b sum to 9,−4 with b parallel to 5, 3 and a orthogonal to 5, 3 . Find a and b. 27. Find the distance from the point ( 8.− 4 ) to the line 3x − 8y = 48 . 28. Find the acute angle formed by the lines 3x + 2y = 8 and 9x − 5y = 4 using vectors. Turkington

29. Find all values of k for which the vectors 2k, k − 2 and 5k, 4 − 3k form an acute angle. 30. Given that a ⋅ b = −54 , b = 14 , θ b = 2π 3 , and the angle between a and b is 5π 6 , find all possible vectors a . 31. Find the exact value of the area of the triangle determined by 4,−6 and −8,−3 without a calculator. 32. Create a formula that generates a sequence of complex numbers that form a spiral with the following properties: the initial complex number has an argument of 5π 4 and modulus of 2 2 ; each new point in the spiral has a modulus 5/3 the previous points modulus and an argument π 6 more than the previous point’s. 33. Find the area of the regular 24-gon whose vertices are the twenty-four 24th roots of 4096 2 − 4096 2i . Answer might be ridiculously small or maybe not. 34. Find, correct to three decimal places, the 5th roots of the complex number −125 − 322i .

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