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Trigonometry Ch 1
| Term | Definition |
|---|---|
| A ray is defined as ___. | a point on a line together with all points of the line on one side of that point |
| An angle is defined as ___. | the union of two rays with a common endpoint |
| The common endpoint of an angle is called the ___. | vertex |
| The fixed ray of an angle is the ___ side. | initial |
| The rotated ray of an angle is the ___ side. | terminal |
| An angle whose vertex is the center of a circle is called the ___ angle. | central |
| The arc through which the terminal side of a central angle moves is called the ___. | intercepted arc |
| An angle located in a Cartesian coordinate system with the vertex at the origin and initial side on the x axis is said to be in ___. | standard position |
| An angle is denoted with ___. | α, β, etc. |
| The measurement of an angle is denoted with ___. | m(α) |
| 1/360 of a circle is a ___. | degree |
| A positive angle goes ___ and a negative angle goes ___. | counterclockwise, clockwise |
| 0>m(α)>90 is called a/an ___ angle. | acute |
| m(α)=90 is called a/an ___ angle. | right |
| 90>m(α)>180 is called a/an ___ angle. | obtuse |
| m(α)=180 is called a/an ___ angle. | straight |
| An angle in standard position is said to lie in the quadrant where ___. | its terminal side lies |
| A ___ angle has its terminal side on an axis. | quadrantal |
| T or F? Straight and right angles are quadrantal angles. | T |
| Two angles whose terminal angles are in the same position are called ___ angles. | coterminal |
| Coterminal measures differ by multiples of ___ degrees. | 360 |
| Coterminal angle: m(β) = m(α) + ___ where k = ___. | k360, number of rotations |
| Which quadrant is bottom left? | III |
| Each degree is divided into ___ equal parts called ___. | 60, minutes |
| Each minute is divided into ___ equal parts called ___. | 60, seconds |
| A second is what fraction of a degree? | 1/3600 |
| What angle is 59°59'60"? | 60° |
| A circle with a radius of 1 (no unit) is called a ___. | unit circle |
| The circumference (C) of a unit circle is defined by the formula ___. | 2π (C = 2πr = 2π(1) = 2π) |
| The radian measure is the measure of ___. | the intercept arc directed length |
| Directed length means the length is either ___ or ___. | positive, negative |
| m(α)= ___ radians | s |
| 2π rad = ___° | 360 |
| π rad = ___° | 180 |
| 360° = ___ rad (digits) | 6.28 |
| 180° = ___ rad (digits) | 3.14 |
| The arc length formula is ___. | s = αr (s=arc length, α=radians, r=radius) |
| Area of a sector formula is ___. | A = (αr²)/2 |
| For an object moving in a circle, there are 2 types of velocity; ___ velocity and ___ velocity. | angular, linear |
| For one revolution an object moves ___ radians. | 2π (6.28) |
| We express angular velocity in ___ per unit of time. | radians |
| T or F? Angular velocity and linear velocity are unrelated. | True. Angular velocity is only concerned with revolutions per time not the linear speed of the object. |
| Angular velocity is given by the formula ___. | ω = α/t (e.g., rpm, rad/sec, rad/min, degrees/hour, etc.) |
| Linear velocity in a circle is given by the formula ___. | v = s/t (i.e., v = d/t) or v = αr/t (where s = αr) |
| Linear velocity in terms of angular velocity is given by the formula ___. | v = rω (v = αr/t, v = r(α/t)) |
| sin = ___ | y/r (opp/hyp) (NOTE: r = hypotenuse not radius!) |
| cos = ___ | x/r (adj/hyp) |
| tan = ___ | y/x (opp/adj) |
| csc = ___ | r/y (hyp/opp) |
| sec = ___ | r/x (hyp/adj) |
| cot = ___ | x/y (adj/opp) |
| Since x = 0 for any point on the y-axis, ___ and ___ are undefined for any angle that terminates on the y-axis. | tan, sec |
| Since y = 0 for any point on the x-axis, ___ and ___ are undefined for any angle that terminates on the x-axis. | csc, cot |
| Trig functions are ___. | ratios |
| The reciprocal of sin is ___. | csc |
| The reciprocal of cos is ___. | sec |
| The reciprocal of tan is ___. | cot |
| 1/(sin α) = ___. | csc |
| 1/(cos α) = ___. | sec |
| 1/(tan α) = ___. | cot |
| T or F? Angles of the same proportion, regardless of size, will have the same values for the trig fxns. | True |
| sin 30 = ___. | 1/2 |
| cos 30 = ___. | √3/2 |
| tan 30 = ___. | √3/3 |
| sin 45 = ___. | √2/2 |
| cos 45 = ___. | √2/2 |
| tan 45 = ___. | 1 |
| sin 60 = ___. | √3/2 |
| cos 60 = ___. | 1/2 |
| tan 60 = ___. | √3 |
| What is the mnemonic for remembering the sign of a fxn in each quadrant? What does it mean? | All students take calculus. All are (+) in Quad I, sin and csc are (+) in II, tan and cot are (+) in III, cos and sec are (+) in IV |
| If an angle lies in quadrant II, the sec will be ___ (+ or -). | (-) |
| If an angle lies in quadrant III, the cot will be ___ (+ or -). | (+) |
| If an angle lies in quadrant IV, the sec will be ___ (+ or -). | (+) |
| sin-¹(1/2) = ___. | 30° |
| sin-¹(√2/2) = ___. | 45 |
| sin-¹(√3/2) = ___. | 60 |
| cos-¹(1/2) = ___. | 60 |
| cos-¹(√2/2) = ___. | 45 |
| cos-¹(√3/2) = ___. | 30 |
| tan-¹(√3/3) = ___. | 30 |
| tan-¹(1) = ___. | 45 |
| tan-¹(√3) = ___. | 60 |
| csc 30 = ___. | 2 |
| csc 45 = ___. | √2 |
| csc 60 = ___. | 2√3/2 |
| sec 30 = ___. | 2√3/3 |
| sec 45 = ___. | √2 |
| sec 60 = ___. | 2 |
| cot 30 = ___. | √3 |
| cot 45 = ___. | 1 |
| cot 60 = ___. | √3/3 |
| x coordinates on the unit circle are the ___ of the angle. | cos |
| y coordinates on the unit circle are the ___ of the angle. | sin |
| Radians measure ___ around the circle and degrees measure ___. | arc length of the unit circle, angles |
| Besides y/x, the tan of an angle can also be calculated by the ___/___. | sin/cos |
| Besides x/y, the tan of an angle can also be calculated by the ___/___. | cos/sin |
| The sum of the angles of a triangle always equals ___°. | 180 |
| The angle of ___ for a point is the angle between the observer and the ground to a point ABOVE the gound. | elevation |
| The angle of ___ for a point is the angle between a vector from the observer to a point BELOW the observer and a horizontal line parallel with the ground at the level of the observer. | depression |
| The Fundamental Identity of trig is the equation ___. | sin² α + cos² α = 1 |
| The Fundamental Identity solved in terms of cos is ___. | sin α = ±√(1 - cos² α) |
| The Fundamental Identity solved in terms of sin is ___. | cos α = ±√(1 - sin² α) |
| For any nonquadrantal angle, the ___ angle for θ is the positive acute angle θ' formed by the terminal side and the nearest x-axis. | reference |
| T or F? The sin, cos, tan, etc. of any angle is the same as the reference angle aside from possibly the sign. | True |
| T or F? The angle of elevation and the angle of depression are always equal if there is an observer at the ground and at the top. | True. The angle of depression is between a downward vector and a horizontal line that is parallel to the ground. It is NOT between the downward vector and the vertical line. |
| T or F? The angle of depression is NOT made suing the vertical line. | True. It is with a horizontal line parallel with the ground. |
Created by:
drjolley
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