Download Test #2 Review Sheet (Chapter 5, 6.1, 6.2)

Test #2 Review Sheet (Chapter 5, 6.1, 6.2)
5.1: Angles
• Given a point and line, define ray, vertex of ray, angle, vertex of angle, initial side of an angle, terminal side of an angle
• Measuring Angles (in rotations, degrees, degrees/minutes/seconds, grads)
• Be able to convert from degrees to degrees/minutes/seconds (DMS) and DMS to degrees
• Be able to convert from degrees to rotations and rotations to degrees
• Acute, Right, Obtuse, Straight Angles; Complementary and Supplementary Angles
• An angle in standard position, Quadrantal Angles, Coterminal Angles
• First Quadrant Angles, Second Quadrant Angles, Third Quadrant Angles, Fourth Quadrant Angles
• Be able to apply, define, and provide a measurement of an angle in standard position
6.1: Radian Measure
• Be able to state and apply the definition of radian measure; note that radians are “unitless” (have no units)
• Be able to convert from radians to degrees and degrees to radians; be able to convert from radians to/from rotations
• Be able to find the arc length of a circle of given radius subtended by a given angle
• Be able to calculate the arc length, perimeter and area of a sector of a circle.
6.2: Unit Circle and Circular (Trigonometric) Functions
• State/apply definition of trigonometric functions of angles in standard position using unit circle (radian measures allowed)
• Relating sine and cosine to measures of line segments on the unit circle
• Know the trigonometric function value and the radian measure of the
o good angles: π/6 radians (30 degrees) , π/4 radians (45 degrees) and π/3 radians (60 degrees)
o any angle which has a good angle as its reference angle.
• Be able to calculate linear and angular speeds of points on a circle/disk/wheel
5.3: Evaluating Trigonometric Functions
• Relate/apply unit-circle definition of trigonometric functions of an acute angle to ratios of side lengths in a right triangle
• Cofunctions and Cofunction identities: e.g. cos(A) = sin(R – A) where R is a right angle measured in same units as angle A
• Know the trigonometric function values and the radian measure of the good angles
o Good Angles: π/6 radians (30 degrees) , π/4 radians (45 degrees) and π/3 radians (60 degrees)
• Reference Angles, Bowtie Rule: Given a terminal side in the first quadrant, there is a terminal side in each of the other
quadrants that shares its trigonometric function values (up to the sign (+/-))
• Finding trigonometric function values of any angle having a good angle as its reference angle
• Finding all angles in a given interval with a given trigonometric function value (primarily when related to good angles)
• Given a trigonometric function value of a non-quadrantal angle in standard position and some information to determine the
quadrant for this angle, be able to find the exact values of the other five trigonometric functions.
• Be sure the calculator is in the right mode (degree mode, radian mode) when approximating trigonometric function values
• Inverse trigonometric function informally used for acute angles
5.4 Solving Right Triangles
• Triangles have six measures (three angle measures and three side lengths)
• Solving a triangle: Given some of these measures (often enough to uniquely define a triangle), find the unknown measure(s).
• When solving a right triangle with vertices A, B, and C,
o one of the angles is a right angle (typically assume this is the angle with vertex C);
o also Pythagorean theorem applies a^2 + b^2 = c^2 (when C is the vertex of the right angle)
o the sum of the measures of all angles in a triangle is the measure of a straight angle
o the sum of the measures of angles with vertices A and B is a right angle (when the right angle has vertex C)
• Solving right triangles given a labeled drawing of the triangle (assuming enough information is given)
• Solving applications with lurking right triangles, angles of elevation and depression, bearings in both formats (clockwise
from north, and N/S measure E/W), other examples as well
5.2: Trigonometric Functions
• Relate unit-circle definition of trigonometric functions to an angle in standard position and a non-vertex point P = (a,b) on its
terminal side in terms of the coordinates (a,b) and the (positive) distance (usually called r) from P to the vertex of the angle.
• Be able to state and apply the expressions (in terms of a, b, and r) of the six trigonometric functions
• Be able to compute all trigonometric function values of an angle in standard position given a point P on its terminal side
• Be able to state and apply the fundamental identities (reciprocal identities, quotient identities, pythagorean identities)
• Know all the trigonometric function values and the measures of the quadrantal angles (in radians, degrees, rotations)
o 0, 90, 180, and 270 degrees as well as any angle which is coterminal (shares a terminal side) with a quadrantal angle
• Know/apply trigonometric function values in terms of points on circles of positive radius ( r denotes the radius of the circle)
• Ranges of the trigonometric functions and whether equations like sinA = 1.2 and sinA = 0.789 have solutions
• Given the exact value of exactly one of the trigonometric functions of an angle in standard position and enough information
to identity the quadrant of the angle, be able to find the exact value of the other five trigonometric functions of the angle.