# Math 1060 Trigonometry Course Objectives

Trigonometry Course Objectives

1. Give the right triangle definition of the trigonometric functions.
2. Solve trigonometric equations
3. Evaluate the trigonometric functions without a calculator at multiples of the references angles p/6, p/4, p/3, and p/2.
4. Graph trigonometric functions including phase shifts, amplitudes, and periods.
5. Prove trigonometric identities; use trigonometric identities to simplify trigonometric expressions.
6. Use the Law of Sines and Cosines to solve application problems.
7. Write the trigonometric form of complex numbers and use De Moivre’s Theorem.
8. Describe the construction of the inverse trigonometric functions, describe their domains and ranges, and know how to use a calculator to solve for angles using inverse trigonometric functions.
9. Graph Conic Sections; parabolas, ellipses, and hyperbolas.
10. Carry out conversions between polar and rectangular coordinates; write the polar equations of conics.

Trigonometric Functions

A student should be able to:

1. Determine complements and supplements of angles given in degrees or radians.
2. Give the measure (in both radians and degrees) of an angle in standard position.
3. Convert angles measured in degrees to its equivalent DMS measure.
4. Convert each DMS measure to its equivalent degree measure.
5. Convert degree measure to radian measure.
6. Convert radian measure to degree measure.
7. Determine the central angle of a circle subtended by a given arc.
8. Find the length of an arc which subtends a central angle of a circle with given radius.
9. Convert between angular speed and linear speed.
10. Find the area of a sector of a circle given the radius and central angle.
11. Find the values of the six trigonometric functions of an angle in a right triangle given the lengths of the sides.
12. Solve application problems involving right triangles.
13. Compute the exact values of the six trigonometric functions of the standard angles.
14. Find the reference angle of a given angle.
15. Use reference angles to compute the trigonometric functions of angles.
16. Use the wrapping function to define the trigonometric functions of real numbers.
17. Use the fundamental trigonometric identities to simplify trigonometric expressions.
18. Solve application problems using trigonometry.
19. State the domain and range of a trigonometric function.
20. Determine whether a trigonometric function is even, odd, both or neither.
21. Determine the period of a trigonometric function.
22. Determine the amplitude of a sine or cosine function.
23. Determine the phase shift of a trigonometric function.
24. Sketch the graph of a trigonometric function using transformations.
25. Give a formula for a trigonometric function given its graph.

Trigonometric Identities and Equations

A student should be able to:

1. Simplify expressions using reciprocal identities, ratio identities, Pythagorean identities and odd even identities.
2. Verify trigonometric identities by a variety of methods, including changing to sines and cosines, using a Pythagorean identity, factoring, multiplying by a conjugate or rewriting in terms of sines and cosines.
3. Use sum, difference, co-function, double-angle, half-angle, power reducing, product-to-sum and sum-to-product identities to simplify and/or evaluate a trigonometric expression.
4. Use sum, difference, co-function, double-angle, half-angle, power reducing, product-to-sum and sum-to-product identities to verify a trigonometric identity.
5. Use sum and difference identities to find reduction formulas.
6. Use power reducing identities to evaluate or simplify a trigonometric expression.
7. Use power reducing identities to verify an identity or evaluate a trigonometric function.
8. Derive power reducing identities from double-angle formulas.
9. Evaluate expressions involving inverse trigonometric functions.
10. Evaluate the composition of a function and its inverse.
11. Sketch graphs of inverse trigonometric functions.
12. Verify trigonometric identities which involve inverse trigonometric functions.
13. Solve trigonometric equations using inverse functions.
14. Solve trigonometric equations involving multiple angles.
15. Solve trigonometric equations by factoring, squaring each side and using the quadratic equation.

Applications of Trigonometry

A student should be able to:

1. Solve triangles using the Law of Sines.
2. Solve application problems involving the Law of Sines.
3. Solve triangles using the Law of Cosines.
4. Solve application problems involving the Law of Cosines.
5. Correctly choose between the Law of Sines and the Law of Cosines when solving a triangle.
6. Find the area of a triangle using the Law of Sines and the Law of Cosines.
7. Use Heron’s Formula to find the area of a triangle.
8. Write a vector in component form.
9. Find the magnitude and direction angle of a vector.
10. Compute sums, differences and scalar multiples of a vector.
11. Determine whether two vectors are parallel or orthogonal.
12. Use vectors to solve application problems.
13. Find the dot product of two vectors.
14. Determine the angle between two vectors.
15. 15.  Compute the projection of one vector onto another.

Complex Numbers

A student should be able to:

1. State the definition of a Complex Number.
2. Write a complex number in standard form.
3. Add, subtract, multiply and divide two complex numbers.
4. Compute powers of i.
5. Write a complex number in trigonometric form.
6. Find the product and quotient of two complex numbers given in trigonometric form.
7. Use DeMoivre’s Theorem to compute the power of a complex number.
8. Find roots of complex numbers using DeMoivre’s Theorem.

Topics in Analytic Geometry

A student should be able to:

1. Graph parabolas, ellipses and hyperbolas in standard form.
2. Complete the square to put a conic into standard form.
3. Use the Rotation Theorem for Conics to determine the angle through which the axes have been rotated.
4. Graph a rotated conic using the Rotation Theorem.
5. Find the polar coordinates of a point given in rectangular coordinates.
6. Find the rectangular coordinates of a point given in polar coordinates.
7. Convert a polar equation to rectangular coordinates.
8. Convert a rectangular equation to polar coordinates.
9. Graph equations given in polar coordinates.