A function value and a quadrant are given. Find the other five function values.

EunoR 2021-09-24 Answered
A function value and a quadrant are given. Find the other five function values. Give exact answers, uing radicals as needed. Rationalize all denominators.
\(\displaystyle{\cot{\theta}}=-{4}\), Quandrant 4

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Plainmath recommends

  • Ask your own question for free.
  • Get a detailed answer even on the hardest topics.
  • Ask an expert for a step-by-step guidance to learn to do it yourself.
Ask Question

Expert Answer

Arnold Odonnell
Answered 2021-09-25 Author has 8362 answers
It is given that, \(\displaystyle{\cot{\theta}}=-{4}\)
Compute the other five functional values as follows.
\(\displaystyle{{\csc}^{{2}}\theta}-{{\cot}^{{2}}\theta}={1}\)
\(\displaystyle{\csc{\theta}}=\sqrt{{{1}+{{\cot}^{{2}}\theta}}}\)
\(\displaystyle{\csc{\theta}}=\sqrt{{{1}+{\left(-{4}\right)}^{{2}}}}\)
\(\displaystyle{\csc{\theta}}=-\sqrt{{{17}}}\)
Compute the value of \(\displaystyle{\sin{\theta}}\) as follows.
\(\displaystyle{\sin{\theta}}={\frac{{{1}}}{{{\csc{\theta}}}}}\)
\(\displaystyle{\sin{\theta}}=-{\frac{{{1}}}{{\sqrt{{{17}}}}}}\)
\(\displaystyle{\sin{\theta}}=-{\frac{{\sqrt{{{17}}}}}{{{17}}}}\)
Compute the value of \(\displaystyle{\cos{\theta}}\) as follows.
\(\displaystyle{\cot{\theta}}={\frac{{{\cos{\theta}}}}{{{\sin{\theta}}}}}\)
\(\displaystyle{\cos{\theta}}={\cot{\theta}}\cdot{\sin{\theta}}\)
\(\displaystyle{\cos{\theta}}=-{4}{\left(-{\frac{{\sqrt{{{17}}}}}{{{17}}}}\right)}\)
\(\displaystyle{\cos{\theta}}={\frac{{{4}\sqrt{{{17}}}}}{{{17}}}}\)
Compute the value of \(\displaystyle{\sec{\theta}}\) as follows.
\(\displaystyle{\sec{\theta}}={\frac{{{1}}}{{{\cos{\theta}}}}}\)
\(\displaystyle{\sec{\theta}}={\frac{{{17}}}{{{4}\sqrt{{{17}}}}}}\)
\(\displaystyle{\sec{\theta}}={\frac{{\sqrt{{{17}}}}}{{{4}}}}\)
Compute the value of \(\displaystyle{\tan{\theta}}\) as follows.
\(\displaystyle{\tan{\theta}}={\frac{{{1}}}{{{\cot{\theta}}}}}\)
\(\displaystyle{\tan{\theta}}=-{\frac{{{1}}}{{{4}}}}\)
Have a similar question?
Ask An Expert
44
 

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2021-09-06
If \(\displaystyle{\sin{{\left(\theta\right)}}}=-{\frac{{{1}}}{{{4}}}}{\sin{}}\) and \(\displaystyle\theta\) is in the 3rd quadrant, find \(\displaystyle{\cos{{\left(\theta\right)}}}\)
asked 2021-09-10
Find the absolute maximum and absolute minimum values of f on the given interval. Give exact answers using radicals, as necessary.
t-(cube root of t) in [ -1,5]
asked 2021-09-17
Find the derivative for the given function. Write your answer using positive and negative exponents and fractional exponents instead radicals.
\(\displaystyle{h}{\left({x}\right)}={\left({\left({6}{x}^{{-{4}}}-{6}{x}+{9}\right)}{\left({7}{x}^{{2}}+{9}{x}+{8}\right)}\right)}^{{{\frac{{{1}}}{{{2}}}}}}\)
asked 2021-09-14
The supply function for a product is given by p = 20 + 100 radical 2x + 9, where x is the number of units supplied and p is the price in dollars. If the price is increasing at a rate of $1 per month, at what rate is the supply changing when x=20?
asked 2021-09-18
Determine the value of the variable for which the expression is defined as real number.
\(\displaystyle{\left({\frac{{{1}}}{{{x}^{{2}}-{2}{x}-{63}}}}\right)}^{{\frac{{1}}{{2}}}}\)
asked 2021-09-10
Antiderivatives of radical function and explain the solution
\(\displaystyle\int{\left({3}\sqrt{{{x}}}+{7}\right)}{\left.{d}{x}\right.}\)
asked 2021-09-29
Model the following data using an exponential function of the form \(\displaystyle{f{{\left({x}\right)}}}={A}{b}^{{x}}\) . Set up a system of equations, and solve it to get A and b.
f(x) is exponential and goes through the points (1, 2) and (4, 6).
...