Question

Find to the nearest ten thousandth, the radian mesasure of theta of a first quadrant angle with the given funtion value..... csc theta=2.346

Answer 1

Do i just go onto my calculator and do the inverse of sin^-1(2.346)?

Answer 2

1/sin^1. csc is the reciprocal of sin.

Answer 3

so it would be sin^-1(1/sin2.346) and press enter right?

Answer 4

@kropot72 Am I right?

Answer 5

If you are familiar with series you can expand it as a taylor series and find the value with the required accuracy. Your way does work too

Answer 6

Im not familiar with this"taylor series" but thank you for the clarity, I think ill use the calculator way, thank you!

Answer 7

@Life What value did you get for theta?

Answer 8

i didnt get it from anywhere its given

Answer 9

The given value is the cosec of theta. What value for the angle theta did you get when you used your calculator as described?

Answer 10

i actually got an error and so i did sin^-1(1/2.346) and i got a decimal from that, is it correct and my calculator is in radian mode

Answer 11

You calculator must be in degree mode. You should get the value of 25.23028246 degrees for theta.
To convert to radians divide the value of theta in degrees by 180 and multiply the result by pi.

Answer 12

did you get .4403515...

Answer 13

would i multiply by 180 and divide by pi for every question, like if it were regular trig funtions like sin cos and tan

Answer 14

You are correct. Theta = 0.4403515 radians
You must first find the value of the angle in degrees. This would require using the inverse trig function to find the angle in degrees if you have the sine, cos or tan etc.
Next degrees are converted to radians by dividing by 180 and then multiplying the result by pi.

Answer 15

what about if the question was cos theta=0.5379

Answer 16

would i do exactly as you said above?

Answer 17

\[\theta=\cos^{-1}0.5379\]
You need to set your calculator to degree mode. The use the cos^-1 function to find theta. Please post the result here.

Answer 18

57.459203...

Answer 19

why am i using inverse if thats just a regular trig funtion?

Answer 20

@kropot72

Answer 21

Your result 57.459203 degrees is correct.
You are given that cos theta=0.5379. Cosine is a trig ratio. To find the measure of theta in radians, given the cosine of theta, it is first necessary to find the value of theta in degrees. The meaning of the inverse trig function cos^-1 0.5379 is 'the angle in degrees that has the cosine value 0.5379'.

Answer 22

So to conclude, with a general statement, when wanting to find out the radian measure in degrees, we always use the inverse trig func

Answer 23

It is only necessary to use the inverse trig function when you are given the trig ratio of the angle concerned.
For example if we are given sin theta = 1. Find the value of theta in radians:
\[\sin^{-1} 1=90\ degrees\]
\[\theta=90\ degrees=\frac{90}{180}\times \pi=\frac{\pi}{2}\ radians\]

Answer 24

If it is given that theta = 180 degrees. Find theta in radians.
\[\theta=180\ degrees=\frac{180}{180}\times \pi=\pi\ radians\]

Answer 25

I got confused, please give me some time to understand everything.

Answer 26

Back to the question where i asked for the cos of theta=0.5379, you said that the answer was 57.459203...but this is the answer before i divide by 180 and multiply by pi, isnt the final answer 1.00285?

Answer 27

\[\frac{57.459203}{180}\times \pi=can\ you\ calculate?\]

Answer 28

when you calculate the above, you get .3192177953, after that I multiply by pi and I get 1.002852281, is that the final answer because before you said that 57.459203 was the answer and I think you may have made a mistake.

Answer 29

Yes the final answer is\[\theta=1.002852278\ radians\]

Answer 30

Our answers are off

Answer 31

the final three numbers are different, I got 281 and you got 278

Answer 32

I confirmed that 57.459203 is the value of theta in degrees. I did not say that 57.459203 is the final answer.
Do not worry about the difference in the three least significant figures of our results.

Answer 33

The answer needs to be given to the nearest ten thousandth. In that case both our answers are; theta = 1.00285 radians

Answer 34

My mistake, I just have one more question, how do I find the exact function value of an angle that is given in radians. For example cos 2(pi)/3 and sec(pi)/3.

Answer 35

For the first one, cos2(pi)/3, would i simply input cos(120) and get the answer?

Answer 36

Yes, if your calculator is set to degrees. If you calculator is set to radians you can enter cos((2 * pi)/3)

Answer 37

I got -.5

Answer 38

I think it needs to be in radical form

Answer 39

which equals to -(pi)/6?

Answer 40

oh thats wrong I meant radical 3/2

Answer 41

Im not sure actually, please explain

Answer 42

cos 120 = cos (180 - 60) = -cos 60 = -0.5

Answer 43

How do I figure out -0.5 in radical form?

Answer 44

\[-0.5=-\frac{1}{2}\]
A radical form does not exist for 1/2

Answer 45

Never mind, I figured it out, back to the other topic, if cot theta=0.3276, what is the radian measure? Is it 1.2542?

Answer 46

You asked "how do I find the exact function value of an angle that is given in radians?"
The simplest way is to set your calculator to radians. Then to find cos 2(pi)/3 you enter cos((2 * pi)/3) and should get the answer -0.5.

Answer 47

Yea, thanx again, I actually noticed that I went back and read what you wrote, do you think you could address the last question I asked which can be found above.

Answer 48

cot theta = 0.3276. Therefore tan theta = 1/0.3276.
\[\theta=\tan^{-1} \frac{1}{0.3276}\]
When you have found the value of theta in degrees you convert to radians by dividing by 180 and multiplying the result by pi.

Answer 49

In that case, my answer is right.

Answer 50

If f(x)=sin(1/3x), find f(pi/2)

Answer 51

Is the answer 92?

Answer 52

The answer is not correct. The maximum value of the sine function is 1, therefore 92 is not correct.

Answer 53

Is it .9993?

Answer 54

If f(x)=sin(1/3x), find f(pi/2)
Is the following correct?
\[f(x)=\sin \frac{1}{3}x,\ find\ f(\frac{\pi}{2})\]

Answer 55

That is correct, the 1/3x is in parenthesis but that doesn't make a difference.

Answer 56

Is the following correct?
\[f(x)=\sin (\frac{1}{3x})\]

Answer 57

the x is lined up with the division sign, but thats all, everything else is fine

Answer 58

\[f(x)=\sin (\frac{1}{3}x)\]
\[f(\frac{\pi}{2})=\sin (\frac{1}{3}\times \frac{\pi}{2})=\sin (\frac{\pi}{6})\]
\[\frac{\pi}{6}\ radians=30\ degrees\]
\[\sin 30degrees=you\ can\ calculate\]

Answer 59

oh wow i got that initially but then changed it because I had thought that we had to have to same denominator but now I realize that's only when we are adding. Its easy thanks for showing me. I have one or two more questions i'd like to show you, it's sort of a new topic but I was absent on the day my teacher explained it to us, hopefully you can help me with it quikly. Thank you for everything, Im seriously grateful :)

Answer 60

You're welcome :) Sorry, i must log out now. Please post as new questions.

Answer 61

Theta is the radian measure of a central angle that intercepts an arc length, s, in a circle with a radius of length, r. If , s=6 and r=1, find theta

Answer 62

@hartnn dude help me quikly please.

Answer 63

@hartnn the question is the most recent reply

Answer 64

s= r* theta
where theta is in radians.

Answer 65

They gave me s, does that mean theta is 6?

Answer 66

yes, theta = 6 radians to be precise.

Answer 67

the next one if if theta=4.5, and s=1.6, find r, soo would it be a negative number?

Answer 68

1.6=r x 4.5

Answer 69

how would i find r?

Answer 70

length of arc s is just the product or radius r and theta angle in radians.
so, s= r * theta
1.6 = r *4.5 [if theta =4.5 is given in radians]
r = 1.6/4.5 =.... ?

Answer 71

I got .355555555556

Answer 72

is that what you got?

Answer 73

yes :)

Answer 74

Awsome just one, just one more, its if s=18, and theta=6(pi)/5, find r, ill try and do it, give me a sec

Answer 75

.083333?

Answer 76

how ?

Answer 77

6(pi)/5=216

Answer 78

and so i did 18/216

Answer 79

and i got the answer

Answer 80

don't convert angle in degrees! we need it in radians only to use that formula....

Answer 81

Ohh so what do i do?

Answer 82

Is it 4.7746...

Answer 83

r= 18 / [6 pi /5] = [18*5]/ [6pi]
yes! 4.7746 is correct! :)

Answer 84

YES!!!!!! Lol thanks man! Seriously appreciate it!

Answer 85

welcome ^_^