Trigonometry

Semester 2 of Algebra 2/Trigonometry

1. Solving Quadratics
2. Trigonometry ** Please note: the applications of Trigonometry may be studied in the 3nd semester due to time contraints**

I. Quadratics

1. Use the discriminant to determine the number and nature of the roots of a quadratic equation and the number of x-intercepts

2. Determine the sum and product of the roots of a quadratic equation by examining its coefficients

3. Determine the quadratic equation, given the sum and product of its roots (using both real roots and
complex roots)

4. Applications of quadratic word problems, i.e. finding the maximum point or minimum point of a quadratic equation.

5. Approximate the solution to polynomial equations of higher degree by inspecting the graph

6. Solve systems of equations involving one linear equation and one quadratic equation algebraically  (includes rational equations that result in linear equation with extraneous roots - directly from NYS curriculum guidelines)

7. Graph Quadratic Inequalities in Two Variables and state a point or points within the solution set

Revisit and Review: Solve a higher degree polynomial using factoring by grouping, know and apply the technique of completing the square and solve quadratic equation, using the quadratic formula. If factoring the sum and difference of two cubes was not covered in the first semester, it should be covered here.

II. Trigonometry

1. Define radian measure

2. Convert between radian and degree measures

3. Express and apply the six trigonometric functions as ratios of the sides of a right triangle

4. Know the exact and approximate values of sine, cosine, and tangent of 0, 30, 45, 60, 90, 180, and 270 degree angles

5. Sketch and use the reference angle for angles in standard position

6. Know and apply the co-function and reciprocal relationships between trigonometric functions

7. Use the reciprocal and co-function relationships to find the value of the secant, cosecant, and cotangent of 0, 30, 45, 60, 90, 180, and 270 degree angles

8. Sketch the unit circle and represent angles in standard position

9. Determine the length of and arc of a circle, given its radius and the measure of its central angle

10. Find the value of trigonometric functions, if given a point on the terminal side of angle ?

11. Restrict the domain of the sine, cosine, and tangent functions to ensure the existence of an inverse function

12. Use inverse functions to find the measure of an angle, given its sine, cosine, or tangent

13. Sketch the graph of the inverses of sine, cosine, and tangent functions

14. Determine the trigonometric functions of any angle, using technology

15. Justify the Pythagorean identities

16. Solve trigonometric equation for all values of the variable from 0 to 360 degrees

17. Determine the amplitude, period, frequency, and phase shift, given the graph or equation of a periodic function

18. Sketch and recognize one cycle of a function of the form y = Asin Bx or y = A cosBx

19. Sketch and recognize the graphs of the functions y = sec?, y = csc?, y = tan?, and y = cot?

20. Write the trigonometric function that is represented by a given periodic graph

21. Solve for an unknown side or angle, using the Law of Sines and/or the Law of Cosines

22. Determine the area of a triangle or a parallelogram, given the measure of two sides and the included angle

23. Determine the solution(s) from SSA situation ? ambiguous case

24. Apply the angle sum and difference formula for trigonometric functions

25. Apply the double-angle and half-angle formulas for trigonometric functions