To solve at an interval (Trigonometry Question)?

Question

Solve the following equation for x in the interval 0 less than or equal to x less than or equal to 2 pi
cos x = -0.32

how do i work this out?

so say if the question asked me for a set in curly braces to two decimal places, would the answer {108.66, 251.34} be correct

Answer 1

There are two answers: one of them falls between pi / 2 and pi, and the other falls between pi and 3pi / 2. You know this because the graph of y = cos x is negative between pi / 2 and 3pi / 2.

Where exactly on the graph does cos x = -0.32? Use your trig table to find out.

On my trig table I find that the cosine of a 71-degree angle is around 0.32; that means that the two angles in question are (180 - 71) and (180 + 71), or 109 and 251. Converting to radians by dividing by 360 and multiplying by 2pi, we get:

x = 1.90 and 4.38

Answer 2

cosx=-o.32
x can be in the second and the third quadrant as cos is negative
if cosx=+0.32 then x=71*15'
since cos is in the second or third quadrant beibg negative it is 180 +/-71*15'
so it can be either 108*45' or 251*15'

Answer 3

i'm fairly particular you have the undertaking written incorrect, as Tan is a function, and ought to't be squared (as quickly as you wrote tan^2x). Assuming you have a TI 80 3 or equivalent/above, you're arranged to circulate into the equation into the y-equals menu (with it equaling y fairly of 0), set the x window to certainly shrink than 0, and only above 2pi. y window only needs to have the x-axis seen. Use calculate 0/answer for each little component of the graph that seems to bypass the x-axis for that section between 0 and 2pi. Use the right suggestions your calculator provides you, and you have the suggestions. psconfirm your calculator is in Radians mode. on a similar time as you're no longer any greater allowed a graphing calculator, you will ought to maximum ideal the equation, and specify that.

Answer 4

cos x = -0.32
x = cos inverse of - 0.32 which can be calculated with help of calculator
since cos x is negative therefore x lies in second and third quadrant

Answer 5

cos x = -0.32
x= cos^(-1)(-0.32) i.e. cos inverse of -0.32
which on solving either manually or by sci calci we get x=108*40' i.e. 108 degree 40 minutes

Answer 6

use inverse trigonometric table to get answer\\\\
cosx= -.32
or, x=cos^-1(-.32)
Now it is clear for given interval 0<=x<=2pi
x will be lying in second or third quadrant \\
use table to evaluate

Answer 7

193(pi)/320 = -0.31833892805254972747012144510049

Is that close enough?