Problems and Review Materials for Math Xb Gateway 3

The third and final gateway will test your facility with the concepts and calculations of trigonometry, including the differentiation and integration of functions that involve sine and cosine.

The gateway test will have eight questions on it. These questions are divided into six categories (see table below). Each gateway test will feature one question drawn from each of the first four categories, together with two questions on differentiating functions that involve sine and cosine, and two questions on integrating functions that involve sine and cosine.

The first time that the gateway will be given will be during lab on Thursday April 24.
Each test will feature eight questions. A passing grade is seven or eight perfectly correct.
The questions that appear on each test will be drawn from the categories shown in the table below.
Each test will have four questions on the definitions of sine, cosine and tangent, two questions on differentiation and two questions on integration.
If you don't pass the test on the first attempt, you will be able to retake the test from Xa lab leaders through the Math Question Center or else from section leaders during office hours.
Remember that you are not allowed to use a calculator or a page of notes on gateway tetsts.
Remember: You have to pass all of the gateway tests by 5p.m. on Friday May 2. For every gateway test that you have not passed by that time, your final grade in the course will be lowered by one complete letter.

Category	Review Problems and Answers
Unit circle definitions of sine and cosine	Problems on the unit circle definitions of sine and cosine.
Right angle triangle definitions of sine, cosine and tangent	Problems on the right angle triangle definitions of sine, cosine and tangent.
Inverse trigonometric functions using the unit circle definitions	Problems on inverse trigonometric functions from the unit circle definitions of sine and cosine.
Inverse trigonometric functions using the right angle triangle definitions	Problems on the inverse trigonometric functions using the right angle triangle definitions of sine, cosine and tangent.
Derivatives of functions involving sine and cosine	Calculating derivatives of functions involving sine and cosine.
Antiderivatives and integrals involving sine and cosine	Calculating antiderivative for functions that involve sine and cosine.