Grade 12 | Mathematics

Objective: Apply triangle trigonometry to solve problems

Action steps

1. Define and evaluate the six trigonometric ratios.

2. Solve triangle problems where one attribute is missing using trigonometric ratios.

3. Use the Law of Sines and Law of Cosines to solve triangle problems (AAS, ASA, or SSA).

4. Use the Law of Sines and Law of Cosines to model and solve real-world problems.

5. Use triangle trigonometry to model and solve real-world problems, including angles of elevation and depression, and indirect measurement, and areas of triangles.

Objective: Apply geometric vectors to solve problems

Action steps

1. Define a geometric vector.

2. Find the norm (or magnitude) and direction of a geometric vector.

3. Use vectors to model and solve real-world problems, including velocity, force, and air navigation.

Objective: Apply circular and trigonometric functions to solve problems

Action steps

1. Define radian measure and convert angle measures between degrees and radians, including revolutions.

2. Find the measures of co-terminal angles.

3. Find and state the six trigonometric functions of special and quadrantal angles.

4. Find and state the six circular and trigonometric functions.

5. Identify and distinguish between circular and trigonometric functions.

6. Develop basic trigonometric identities.

7. Use trigonometric functions to model and solve real-world problems, including right triangle relations, arc length, speed, and uniform circular motion.

Objective: Apply trigonometric graphs to solve problems

Action steps

1. Graph the sine, cosine, and tangent functions.

2. Identify the domain and range of a basic trigonometric function.

3. Sketch transformations of the sine, cosine, and tangent graphs.

4. Sketch the cosecant, secant, and cotangent functions and their transformations.

5. Identify and sketch the period, amplitude (if any), phase shift, zeroes, and vertical asymptotes (if any) of the six trigonometric functions.

6. Use trigonometric graphs to model and solve real-world problems.

Objective: Apply inverse circular and trigonometric functions to solve problems

Action steps

1. Define the domain and range of the inverse circular functions.

2. Evaluate the inverse circular functions.

3. Define the domain and range of the inverse trigonometric functions and sketch the graph.

4. Evaluate the inverse trigonometric functions.

5. Use inverse functions to model and solve real-world problems.

Objective: Apply trigonometric equations and identities to solve problems

Action steps

1. Apply strategies to prove identities, including Pythagorean, and even and odd identities.

2. Verify trigonometric identities graphically.

3. Use the addition and subtraction identities for sine, cosine, and tangent functions to solve problems.

4. Use the double-angle and half-angle identities to solve problems.

5. Use identities to solve trigonometric equations.

6. Solve trigonometric equations graphically and algebraically.

Objective: Use analytic geometry to solve problems

Action steps

1. Define a circle and write its equation.

2. Analyze and sketch the graph of a circle.

3. Define an ellipse and write its equation.

4. Analyze and sketch the graph of an ellipse.

5. Define a hyperbola and write its equation.

6. Analyze and sketch the graph of a hyperbola.

7. Define a parabola and write its equation.

8. Analyze and sketch the graph of a parabola.

9. Write the equation of and graph a translated conic section.

10. Use conic sections to model and solve real-world problems.

Objective: Use complex numbers and polar equations to solve problems

Action steps

1. Graph complex numbers on the complex plane.

2. Find the trigonometric form of complex numbers.

3. Apply DeMoivre’s Theorem to complex numbers in trigonometric form.

4. Change Cartesian coordinates to polar coordinates and vice versa.

5. Plot points using polar coordinates and graph polar equations.

6. Change equations from rectangular form to polar form and vice versa.

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