Trig Ratios
What sides do you use to find sin?
Opposite/Hyp
Solve the trigonometric equation for all values 0 ≤x<2π. 2sinx+1=0
Convert the polar coordinates (3,0) into rectangular form. Express your answer in simplest radical form.
(3,0)
During a certain time of year, the daily temperature in a certain city, in degrees Fahrenheit follows a periodic pattern, given by the function, T(t)=9.5sin(n/12(t-8)) +62.5, where TT represents the temperature and time tt is measured in hours after 12:00 a.m. (midnight). What is the midline and what does it represent in this context?
The midline is 62.5 degrees Fahrenheit and it represents the days’ average temperature.
What quadrant is tangent negative?
Quadrant 2 and Quadrant 4
what sides do you need to find Cos?
adj/hyp
Solve the trigonometric equation for all values 0≤x<2π 3tanx=−3
5π/6 and 11π/6
Convert the polar coordinates(2√3,0)into rectangular form. Express your answer in simplest radical form.
(2√3,0)
The volume of air in a person’s lungs can be modeled with a periodic function, V(t)=700cos(2n/7(t-2.25)) +1800, where V represents the volume of air, in mL, in a person’s lungs and time t is measured in seconds. What is the minimum and what does it represent in this context?
The minimum is 1100 mL and it represents the minimum air volume.
In what quadrant is sine positive?
Quadrant 1 and Quadrant 2
what is sin(30)?
1/2
Write a sine function that has an amplitude of 3, a midline of 4 and a period of π/2
f(x)=3sin(4x)+4
Convert the polar coordinates(2√3,5π/3)into rectangular form. Express your answer in simplest radical form.
(√3,-3)
During a certain time of year, the daily temperature in a certain city, in degrees Celsius follows a periodic pattern, given by the function T(t)=6.5sin(n/12(t-8.5)) +13.5, where T represents the temperature and time tt is measured in hours after 12:00 a.m. (midnight). What is the maximum and what does it represents in this context.
The maximum is 20 degrees Celsius and it represents the days’ high temperature.
What quadrant is 150 degrees in?
Quadrant 2
whats tan(3π/4)?
-1
Write a cosine function that has a midline of 2, an amplitude of 3 and a period of 6π
f(x)=3cos(1/3x)+2
Convert the polar coordinates(4√3,11π/6)into rectangular form. Express your answer in simplest radical form.
(6,-2√3)
Over the course of a full year, the daylight in a certain city follows a periodic pattern given by the function D(t) = 189cos (π/6(t+0.5) + 770.9 where D represents the average daylight, in minutes, over the course of twenty-four months, and time t represents the number of months after January 1. What is the minimum and what does it represent in this context?
The minimum is 581.9 minutes and it represents the years’ daylight low.
What is 7π/4 in degrees?
315 degrees
what is cos(-270*)
0
For the rotation start fraction, 35π/3,, find the coterminal angle from 0≤θ<2π, the quadrant, and the reference angle.
5/3π
Convert the polar coordinates(6,5π/4)into rectangular form. Express your answer in simplest radical form.
(-3√2,-3√2)
Over the course of a full year, the daylight in a certain city follows a periodic pattern given by the function D(t)=183.95 sin(6π(t−2.5))+666.75 where DD represents the average daylight, in minutes, over the course of twenty-four months, and time tt represents the number of months after January 1. What is the minimum and what does it represent in this context?
The amplitude is 183.95 and it represents the the difference between the years’ minimum and average daylight.
What is 124π in degrees? How many times does it revolve around the unit circle?
22320 degrees and it revolves the unit circle 62 times