Math  /  Trigonometry

Questionnvestigate.
1. Determine approximate solutions for each equation in the interval x[0,2π]x \in[0,2 \pi], to the nearest hundredth of a radian. a) sinx14=0\sin x-\frac{1}{4}=0 b) cosx+0.75=0\cos x+0.75=0 c) tanx5=0\tan x-5=0 d) secx4=0\sec x-4=0 e) 3cotx+2=03 \cot x+2=0 f) 2cscx+5=02 \csc x+5=0

Studdy Solution
Solve the equation 2cscx+5=0 2 \csc x + 5 = 0 .
2cscx=5 2 \csc x = -5 cscx=52 \csc x = -\frac{5}{2}
Since cscx=1sinx\csc x = \frac{1}{\sin x}, we have:
sinx=25 \sin x = -\frac{2}{5}
Use the inverse sine function to find the principal value:
x=arcsin(25) x = \arcsin\left(-\frac{2}{5}\right)
Calculate the approximate value:
x0.41radians x \approx -0.41 \, \text{radians}
Adjust to the interval [0,2π][0, 2\pi]:
x5.87radians x \approx 5.87 \, \text{radians}
Since sine is negative in the third and fourth quadrants, the second solution is:
x=πarcsin(25) x = \pi - \arcsin\left(-\frac{2}{5}\right)
Calculate the approximate value:
x3.55radians x \approx 3.55 \, \text{radians}
The approximate solutions for each equation are:
a) x0.25,2.89 x \approx 0.25, 2.89 b) x2.42,3.86 x \approx 2.42, 3.86 c) x1.37,4.51 x \approx 1.37, 4.51 d) x1.32,4.96 x \approx 1.32, 4.96 e) x2.16,5.30 x \approx 2.16, 5.30 f) x3.55,5.87 x \approx 3.55, 5.87

View Full Solution - Free
Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord