Find derivative of trigonometric function y=(3(1-sin x))/(2cos x)

Question

Question

Answers (1)

Relevant Questions

asked 2021-01-05

Find derivative of trigonometric function \(\displaystyle{y}=\frac{{{3}{\left({1}-{\sin{{x}}}\right)}}}{{{2}{\cos{{x}}}}}\)

See answers (1)

asked 2020-12-02

Find derivative of trigonometric function \(y=(3(1-sin x))/(2cos x)\)

See answers (1)

asked 2020-11-26

Write the trigonometric expression \(\displaystyle{\cos{{\left({{\sin}^{{-{1}}}{x}}-{{\cos}^{{-{1}}}{y}}\right)}}}\) as an algebraic expression (that is, without any trigonometric functions). Assume that x and y are positive and in the domain of the given inverse trigonometric function.

See answers (1)

asked 2020-11-22

Find the derivative of
\(\displaystyle{y}={\sin{{\left(\pi{x}\right)}}}\)

See answers (1)

asked 2021-01-31

Use a calculator to find the value of the trigonometric function \(\displaystyle{\sin{{\left(\frac{{{3}\pi}}{{10}}\right)}}}\) to four decimal places.

See answers (1)

asked 2021-03-06

Given the values for sin t and cos t, use reciprocal and quotient identities to find the values of the other trigonometric functions of t.
\(\displaystyle{\sin{{t}}}=\frac{{3}}{{4}}{\quad\text{and}\quad}{\cos{{t}}}=\frac{\sqrt{{7}}}{{4}}\)

See answers (1)

asked 2021-02-12

The question asks for the exact value of the trigonometric function at the given real number:
\(\displaystyle{\sin{{\left(\frac{{{3}\pi}}{{4}}\right)}}}\)

See answers (1)

asked 2020-12-22

Use a calculator to find the value of the trigonometric function csc 1 to four decimal places.

See answers (1)

asked 2021-02-05

Find the derivative of
\(y=\sin(\pi x)\)

See answers (1)

asked 2021-02-09

Find the values of the other trigonometric functions of theta if \(\displaystyle{\cot{\theta}}=-\frac{{4}}{{3}}{\quad\text{and}\quad}{\sin{\theta}}{<}{0}\).

See answers (1)

Answer 1

Simplify the trigonometric function
\(\displaystyle{y}=\frac{{{3}{\left({1}-{\sin{{x}}}\right)}}}{{{2}{\cos{{x}}}}}\)
\(\displaystyle{y}=\frac{{3}}{{2}}{\left(\frac{{1}}{{\cos{{x}}}}-{\left(\frac{{\sin{{x}}}}{{\cos{{x}}}}\right)}\right)}\)
\(\displaystyle{y}=\frac{{3}}{{2}}{\left({\sec{{x}}}-{\tan{{x}}}\right)}{\left\lbrace\because\frac{{1}}{{{\cos{{x}}}}}={\sec{{x}}}{\quad\text{and}\quad}\frac{{{\sin{{x}}}}}{{{\cos{{x}}}}}={\tan{{x}}}\right\rbrace}\)
Derivative of trigonometric function:
\(\displaystyle{y}=\frac{{3}}{{2}}{\left({\sec{{x}}}-{\tan{{x}}}\right)}\)
\(\displaystyle\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}=\frac{{d}}{{{\left.{d}{x}\right.}}}{\left(\frac{{3}}{{2}}{\left({\sec{{x}}}-{\tan{{x}}}\right)}\right)}\)
\(\displaystyle\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}=\frac{{3}}{{2}}{\left(\frac{{d}}{{{\left.{d}{x}\right.}}}{\left({\sec{{x}}}\right)}-\frac{{d}}{{{\left.{d}{x}\right.}}}{\left({\tan{{x}}}\right)}\right)}\)
\(\displaystyle\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}=\frac{{3}}{{2}}{\left({\left({\sec{{x}}}\cdot{\tan{{x}}}\right)}-{{\sec}^{{2}}{x}}\right)}{\left\lbrace\because\frac{{x}}{{{\left.{d}{x}\right.}}}{\left({\sec{{x}}}\right)}={\left({\sec{{x}}}\cdot{\tan{{x}}}\right)}{\quad\text{and}\quad}{d}{\left({\left.{d}{x}\right.}\right)}{\left({\tan{{x}}}\right)}={{\sec}^{{2}}{x}}\right\rbrace}\)
The derivative of function is given below
\(\displaystyle\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}=\frac{{3}}{{2}}{\left({\left({\sec{{x}}}\cdot{\tan{{x}}}\right)}-{{\sec}^{{2}}{x}}\right)}\)

Didn’t find what you are looking for?

Find derivative of trigonometric function y=(3(1-sin x))/(2cos x)

Answers (1)

Relevant Questions