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MAC1114 TEST 1 2024-2025 Questions With Correct Answers
Circumference of a circle: -Answer C = 2 pi r
Area of a circle: -Answer A = pi r^
If an object moves at an average speed (rate) r the distance d covered in time t is given by the following formula. - Answer Distance equals = Rate •Time
An angle θ is in ________ _______ if its vertex is at the origin of a rectangular coordinate system and its initial side coincides with the positive x-axis. - Answer An angle θ is in standard position if its vertex is at the origin of a rectangular coordinate system and its initial side coincides with the positive x-axis
A ______ _______ is a positive angle whose vertex is at the center of a circle. - Answer A central angle is a positive angle whose vertex is at the center of a circle.
If the radius of a circle is r and the length of the arc subtended by a central angle is also r, then the measure of the angle is 1 _______. - Answer If the radius of a circle is r and the length of the arc subtended by a central angle is also r, then the measure of the angle is 1 radian.
Arc length formula: - Answer s = rθ
Area of the sector formed by this angle thetaθ is: - Answer A =1/2 r^2 θ.
Converting radians to degrees. (Remember, if it has pi, eliminate it. If it doesn't have pi, give it pi). - Answer x 180/pi
Converting degrees to radians. - Answer x pi/
D°M'S'' - Answer D degrees. M minutes, S seconds
Conversion from D°M'S'' system to X°: - Answer D° (already degree) + M'/60 + S''/ = X°
Conversion from X.YZ° to D°M'S'': - Answer Take X°, it will be D° Take decimal .YZ x 60 (because you're dividing by 1/60) That answer will be M' If you have another decimal, multiply again by 60. That will be your S''
The minute hand of a clock is 9 inches long. How far does the tip of the minute hand move in 40 minutes? - Answer Use arc formula s = r θ We know r = 9 inches, but what about θ? We also know that one revolution around a clock is 2pi. Therefore, 2pi = 60 minutes. So, 40/60 x 2pi = θ Multiply θ by r to give you s.
Formula for angular speed: - Answer w = θ /t
Formula for transverse speed: Manipulate it. - Answer v = s/t v = r θ /t So v= wt
6 inch ---> X rpm HINT: LINEAR SPEEDS ARE EQUAL. FIND ANGULAR FIRST.
- Solution 5 circles around = 5 x 2pi radians = 10pi radians /minute 10 radians per minute is the angular speed Find linear speed now: nr 10pi / minute 62.832 inch/ min Divide by circumference of circle. 62.832/ 2pi x 6 = 1.666 rpm
For a function y =f(x), for each x in the domain, there is - Answer exactly one element y in the range.
If two triangles are similar, then corresponding angles are _____ and the lengths of corresponding sides are _______. - Answer If two triangles are similar, then corresponding angles are
equal and the lengths of corresponding sides are proportional.
What point is symmetric with respect to the y-axis to the point (-2,-3)? - Answer X becomes positive (2, -3)
Equation of the unit circle: - Answer x^2 + y^2 = 1 Given one point, you can find the other.
From (x,y) what will these give you? sin cos tan - Answer sin = y
cos = x tan = x/y
Acronym to remember positive functions in unit circle: - Solution Always Sign T-shirts Carefully (with their reciprocals).
Angles on unit circle thought process: - Solution 0, 90, 180, 270, 360 30, 45, 60 120, 135, 150 210, 225, 240 300, 315, 330
Radians thought process: - Solution 0, pi/2, pi, 3pi/2, 3pi Countdown 6,4,3 bottom/up Remember for quadrants 2, 3, 4 2-3-5, 7-5-4, 5-7-
Coordinate thought process: - Solution Only have three numbers: 3>2> Middle is always 2 Think greater x or y ADD +-
For any angle θ in standard position, let equals=(x,y) be the point on the terminal side of thetaθ that is also on the circle x^2 +y^2 =r^2. Then, sine θ=. cos =. - Answer Sine θ= y/r Cos θ= x/r
sin= - Answer y cos= - Answer x
Is tan odd/even, symmetric? If so, to what? -Answer Odd, Yes to origin.
Function of sin graph -Answer y= A sin(wx) where A= amplitude Period= 2pi/w
The function y= 5 cos (4x) What's amp and period? -Answer A= nw= 2pi / 4
T or F ny= 3sin (-2x) is the same as y= -sin (2x) - Solution
Graph of sin form L to R - Solution Hits (0,0) goes up Amplitude is up and down Period is when hits x axis the second time!
