Complete ALEKS Trigonometry with these practice questions and answers. This guide covers angles, trigonometric functions, identities, inverse functions, and applications.
Q: Terminal vs initial sidedefine Angle
Answer: initial – Ray that the rotation starts onterminal – Ray that the rotation ends onThe distance of that rotation about the vertex of the rays
Q: Positive vs negative angle
Answer: If the rotation moves clockwise, the angle will be negativeCounter clockwise, positive angle
Q: Where does an angle have to “stop”
Answer: It does,t it can rotate past a full revolution
Q: Define coterminal angles
Answer: Angles that share the same terminal side, but no necessarily the same initial side
Q: How many radians is a 360 degree revolution
Answer: 2π
Q: How many radians is 1/4 of a revolution?1/3?
Answer: 2π/4 = π/22π/3
Q: Define standard position of an angle
Answer: vertex at origin and initial side long positive X axis
Q: Quadrantal Angle
Answer: Angles (in std. Position) whose terminal sides coincide with one of the coordinate axesThe degree is an integer multiple of 90°The radian measure is an integer multiple of π/2
Q: reference angles
Answer: the acute angle formed by the terminal side of an angle in standard position and the *x-axis*
Q: trig ratios mnumonicn
Answer: soh cah toa
Q: Which of sine, cosine, or tagent is represented by the (x,y) coordinates where the terminal angle intersects the unit circle
Answer: (cos,sin)
Q: Unit circle, MEMORIZE IT
Answer: use soh cah toamake sure to use the sin⁻¹,cos⁻¹, and tan⁻¹ functions.ex: sin⁻¹(10/2) for triangle with opposite side of length 10 and hypotenuse of length 2
Q: MAGIC HEXEGON
Answer: 1. use pethag. theorem to find the third side2. Use soh cah toa to find the needed basic identites3. use the magic hexegon to find the rest.Just leave it as sqrt(x)/yNOPE
Q: using trigonometric ratios to find unknown angle in a right triangle given length of two sides
Answer: To find unknown angle:180-given-90 = unknownTo find unknown sides:assemble trig ratios, solve for each variable
Q: Finding three of the 6 trig. identities given two sidesWhat do you do when you find yourself with a pathagorean theorem equation that doesn’t square root nicely?Should you rationalize denominators?
Answer: NO, you put it all under 1
Q: Steps to solve right triangles given one side and an angle
Answer: sqrt(2), why?Because this fraction is dividing one whole (2) by some number that multiplied by itself returns 2. The answer to that division is that number, so sqrt(2)
Q: ALL TRIG IDENTITIES
Answer: How many halves in one whole?2
Q: When finding csc, sec, or cot of a xpi/y form angle, do you flip the numerator and denominator?
Answer: sqrt(3)/3fraction divided by a fraction is the numerator multiplied by the denominator with the numerator and denominator of the denominator flipped
Q: 1/(sqrt(2)/2) = ?
Answer: To get a coterminal angle you add or subtract a multiple of 2π or 360⁰, this places the terminal side back at that location, though the angle size is different.place the multiple of 2pi/1, then get common denominator, then add or subtract
Q: 1/(1/2) =
Answer: because 1 pi is divided into 12 pieces, so 24 would be 2pi
Q: (1/2)/(sqrt(3)/2) =
Answer: 4pi/2 is 2pi
Q: Finding coterminal within a given range of angles for a given angle
Answer: The reference angle of a given angle will be that angle minus either pi/2, pi, 3pi/2, or 2pi depending on which quadrant the angle is in.this works because you are subtracting all the quadrant amounts leaving only the value of angle from the start of the quadrant the terminal side is in to said terminal side, the definition of the reference angleIT”S ALWAYS FROM THE POSITIVETERMINAL ANGLE IS THE ANGLE FORMED BY THE TERMINAL SIDE AND THE X AXIS
Q: How is 17pi/12 between 0 and 2pi
Answer: s = rθ1. Convert the given angle to radians if needed2. do the equationjust apply the known parts and do algebra.If you get a number that is “1.3 radians” or something like that, no conversion is needed.
Q: How is 3pi/2 between 0 and 2pi
Answer: When you divide s by r, that gives you the radian fractionNo, for example. 28 = r(.7) -> 28/.7 = 0.68…This 0.68 number is the radian number. Dont round it and finish the problem
Q: Finding the reference angle for a given radian angle
Answer: Radian * 180/pi”180 degrees per radian”
Q: law of sine, finding sides and angles of a non-right triangle when given some sides and angles
Answer: Given that r = sqrt(x^2+y^2), you can calculate the hypotenus (r) with the given point.the x of the point corresponds to the length of the horizontal side of the triangle, the y corresponds to the verticalfrom there the trig ratios are actually normal. soh cah toa