1. ### Consider the equation cos(2.13t)=0.5. Find the smallest positive solution in radians

1. Consider the equation cos(2.13t)=0.5. Find the smallest positive solution in radians and round your answer to four decimal places. 2. Consider the equation tan(2.81t)=10.0. Find the smallest positive solution in radians and round your answer to four decimal places. Please explain. Thank you!

Evaluate Sin^-1√3/2. Enter your answer in radians. I would be pi/3 in radians or 60 degrees in degrees. If you take a look at the unit circle pi/6 has the coordinates (1/2,sqrt(3)/2) When you're dealing with sin it's going to be the value in the y-coordinate thus for sin(pi/3)=sqrt(3)/2 I...
3. ### help needed understanding radians

hello all, I'm just having a bit of a conceptual problem understanding the usage of radians and was wondering if anyone could help me understand in words what I'm missing. I'm trying to teach myself trig so sometimes when the input is just "one way" it's hard for me to conceptualize things. My...

What is pi + 1/3 radians equal to in degrees. Show how you arrived at the answer.
5. ### An angle measuring 5.25 radians is equal to which of the angle measures given below?

An angle measuring 5.25 radians is equal to which of the angle measures given below? Check all that apply. A. 300 degrees 48’ 10” B. 300.80 degrees C. 16.49 degrees D. 16 degrees 24’ Is this right below: 180= pi radians 1 radian=57.29578 5.25 radians would equal both Answer: A and B...
6. ### Finding an angle in radians and finding exact values

Hi I'm really stuck with these two questions would anyone be able to help? a) Given that sec theta=-sqrt2, tan theta=-1 and -pi<theta<pi, find the exact value of the angle theta in radians. Justify your answer. b) Given that -pi<theta<-1/2pi and cos theta =-1/6 use appropriate trigonometric...

Wasn't sure how to justify that. Although, of course, it sort of feels right, because radians are based on actual lengths on a plane, and degrees are mere fractions, as I understand.

I have a question: why is the angle measurement of a 360 degrees = to 2 pi radians and not 2 pi r radians? Why is pi radians = 180 degrees ? Is pi in this case still 3.141....? I am confused why we use pi in radians and some times we do not like in the second example provide here Mathwords...
9. ### Need some clarification regarding radians

I was sitting the other day with my cousin, helping him with his homework, when he asked me what's the deal with these radians. So I took a paper and a pen and tried to recall where did these radians come from, but something is not quite clear for me. Consider the following circle: When the...
10. ### Finding the sum, in radians, of the solutions for x

I am trying to solve a problem from a study manual for the NYSTCE. I think the manual might be breaking some mathematical laws. Someone please throw a life raft. The problem is as follows: What is the sum, in radians, of the solutions for x in the following equation? Tan2x = (3/2)(sec x) The...
11. ### Radians and the Quest to find Theta

I attached a scan of the question giving me trouble as it has a helpful drawing - basically I have to find the radius and height of the cone, and angle of inclination, when the original angle of the radian varies under certain conditions. I'm not just looking for the answer but I do really want...
12. ### Trouble finding reference angles with radians

I am having trouble finding reference angles with radians. For instance: #1) 33pi/4 #2) -23pi/6 How do I go about solving these?

I am converting some radians to degrees. I would assume that sin(1°) = sin(pi/180) yes? Since 1°=pi/180. So by algebraic defaults, this should hold true.. But I am getting strange values in these three calculations: sin-356° - Wolfram|Alpha sin4° - Wolfram|Alpha sin364° - Wolfram|Alpha They...
14. ### How do I find negative radians on the unit circle?

Hello all. For the last 2 hours I've been working on sum and difference problems and cannot seem to get answers that match the book's answers. Here's what i did: sin(-7pi/12) = sin(2pi/12 - 9pi/12) = sin(pi/6 - 3pi/4) = sin(pi/6)cos(3pi/4) - cos(pi/6)sin(3pi/4) = (1/2)(-rad2/2) -...
15. ### Finding areas of sectors using radians

There is a question on the area of a sector of a circle on which I am stuck and was wondering whether anyone could give me a pointer. I have attached an image of the diagram to which the question refers... The diagram shows an arc of ABC of a circle centre o and radius 10cm. Angle AOB =...

A badge is made of a circle centre O, with radius 5cm and a chord AB of length 6cm creating a blue minor segment at the bottom. Give all your answers to 1 decimal place. Find: The angle AOB at the centre The length of the minor arc AB The area of the triangle AOB. The area of the yellow major...