MATH 120 - Trigonometry

3 Credit (3 lecture, 0 lab) 3 Contact Hours [Math Level 5 ]

1. Measure angles using a protractor.
2. Use geometric properties of parallel lines, circles, and geometric figures to find unknown angles.
3. Use geometric properties of similar and right triangles to find unknown sides.
4. Draw angles in standard position in degrees or radians and find angles which are coterminal with the angle.
5. Define the reference angle for any standard angle.

Goal 2:  Use angular measure and arc measure to solve problems involving circles and circular motion.

1. Define a radian.
2. Convert between radians and degrees.
3. Use the formula q= s/r to determine q, s, r from given information.
4. Convert between angular and linear velocity.
5. Solve application problems involving arc length, angular velocity, and area of circular sectors.
6. Determine points on the unit circle corresponding to arc lengths.

Goal 3:  Understand the and apply the trigonometric functions using several definitions.

1. Determine the values of the six trigonometric functions using the point (x, y) in the plane on the terminal side of in standard position.
2. Determine the values of the six trigonometric functions for “special angles” given in degrees or radians without a calculator. “Special angles” are those angles which are quadrantal and also those angles which are multiples of 30 O, 45 O, or 60 O.
3. Define the six trigonometric functions for right triangles.
4. Appropriately use a graphing calculator to solve right triangles.
5. Solve application problems involving right triangle trigonometry.
6. Define the trigonometric functions as circular functions.
7. Determine the sign of all trig functions for each quadrant.
8. Calculate the value of any trig function given another one and the angle’s quadrant.

Goal 4:  Graphically interpret trigonometric functions and their transformations.

1. Graph all six basic trigonometric functions without a calculator.
2. Describe the effect of A, B, C, K for the trigonometric functions in the form K+A (sin, cos, tan) (Bx+c).
3. Use a graphing calculator to graph any trigonometric function in an appropriate window.
4. Determine the equation of a trigonometric function given the graph and the window used to graph the function.

Goal 5:  Apply inverse trigonometric functions and the notation associated with them.

1. Describe the necessary criteria placed on the three basic trigonometric functions so that they have inverses which are also functions.
2. Evaluate inverse trigonometric functions to obtain exact values and decimal approximations in both radian and degree mode.
3. Use inverse trigonometric functions to solve basic trigonometric equations.
4. Graph the three-basic inverse trigonometric functions.

Goal 6:  Utilize, simplify, and verify trigonometric identities.

1. Describe the difference between a conditional equation and identity.
2. Use counter examples and graphing calculations to disprove proposed identities.
3. Know the reciprocal, ratio, Pythagorean and opposite angle identities from memory and use them to simplify trigonometric expressions and verify trigonometric identities involving these identities.
4. Verify identities involving the sum and difference identities, double angle identities and cofunction identities.
5. Determine the exact values for expressions such as cos(+ β), sin( -β), tan (2β), etc.

Goal 7:  Solve trigonometric equations.

1. Solve trigonometric equations using radians or degrees with techniques such as factoring and manipulation with trigonometric identities.
2. Solve trigonometric equations using radians or degrees where the argument of the trigonometric function is a function.
3. Use a graphing calculator to solve trigonometric equations.
4. Write the general solution to trigonometric equations using radians or degrees.

Goal 8:  Solve oblique triangles using the Law of Sines and Law of Cosines

1. Derive the Law of Sines.
2. Use the Law of Sines (including the ambiguous case) and Law of Cosines to solve triangles.
3. Use the Law of Sines and Law of Cosines to solve application problems.
4. Use the Law of Sines and Law of Cosines to determine the area of non-right triangles.