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UVU Math 1060 Trigonometry Course Objectives

**Trigonometry Course Objectives**

- Give the right triangle definition of the trigonometric functions.
- Solve trigonometric equations
- Evaluate the trigonometric functions without a calculator at multiples of the references angles p/6, p/4, p/3, and p/2.
- Graph trigonometric functions including phase shifts, amplitudes, and periods.
- Prove trigonometric identities; use trigonometric identities to simplify trigonometric expressions.
- Use the Law of Sines and Cosines to solve application problems.
- Write the trigonometric form of complex numbers and use De Moivre’s Theorem.
- 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.
- Graph Conic Sections; parabolas, ellipses, and hyperbolas.
- Carry out conversions between polar and rectangular coordinates; write the polar equations
of conics.

**Trigonometric Functions**

*A student should be able to:*

- Determine complements and supplements of angles given in degrees or radians.
- Give the measure (in both radians and degrees) of an angle in standard position.
- Convert angles measured in degrees to its equivalent DMS measure.
- Convert each DMS measure to its equivalent degree measure.
- Convert degree measure to radian measure.
- Convert radian measure to degree measure.
- Determine the central angle of a circle subtended by a given arc.
- Find the length of an arc which subtends a central angle of a circle with given radius.
- Convert between angular speed and linear speed.
- Find the area of a sector of a circle given the radius and central angle.
- Find the values of the six trigonometric functions of an angle in a right triangle given the lengths of the sides.
- Solve application problems involving right triangles.
- Compute the exact values of the six trigonometric functions of the standard angles.
- Find the reference angle of a given angle.
- Use reference angles to compute the trigonometric functions of angles.
- Use the wrapping function to define the trigonometric functions of real numbers.
- Use the fundamental trigonometric identities to simplify trigonometric expressions.
- Solve application problems using trigonometry.
- State the domain and range of a trigonometric function.
- Determine whether a trigonometric function is even, odd, both or neither.
- Determine the period of a trigonometric function.
- Determine the amplitude of a sine or cosine function.
- Determine the phase shift of a trigonometric function.
- Sketch the graph of a trigonometric function using transformations.
- Give a formula for a trigonometric function given its graph.

**Trigonometric Identities and Equations**

*A student should be able to:*

- Simplify expressions using reciprocal identities, ratio identities, Pythagorean identities and odd even identities.
- 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.
- 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.
- Use sum, difference, co-function, double-angle, half-angle, power reducing, product-to-sum and sum-to-product identities to verify a trigonometric identity.
- Use sum and difference identities to find reduction formulas.
- Use power reducing identities to evaluate or simplify a trigonometric expression.
- Use power reducing identities to verify an identity or evaluate a trigonometric function.
- Derive power reducing identities from double-angle formulas.
- Evaluate expressions involving inverse trigonometric functions.
- Evaluate the composition of a function and its inverse.
- Sketch graphs of inverse trigonometric functions.
- Verify trigonometric identities which involve inverse trigonometric functions.
- Solve trigonometric equations using inverse functions.
- Solve trigonometric equations involving multiple angles.
- Solve trigonometric equations by factoring, squaring each side and using the quadratic
equation.

**Applications of Trigonometry**

*A student should be able to:*

- Solve triangles using the Law of Sines.
- Solve application problems involving the Law of Sines.
- Solve triangles using the Law of Cosines.
- Solve application problems involving the Law of Cosines.
- Correctly choose between the Law of Sines and the Law of Cosines when solving a triangle.
- Find the area of a triangle using the Law of Sines and the Law of Cosines.
- Use Heron’s Formula to find the area of a triangle.
- Write a vector in component form.
- Find the magnitude and direction angle of a vector.
- Compute sums, differences and scalar multiples of a vector.
- Determine whether two vectors are parallel or orthogonal.
- Use vectors to solve application problems.
- Find the dot product of two vectors.
- Determine the angle between two vectors.
**15.**Compute the projection of one vector onto another.

**Complex Numbers**

*A student should be able to: *

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

**Topics in Analytic Geometry**

*A student should be able to:*

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

**Additional Information**

Sample 1060 Syllabus (PDF format , word format)

Sample 1060 Homework Set (Excel Format)

**Course Coordinator for Faculty Resources**

Contact Dr. Ya Li, Liya@uvu.edu