Determine the exact value of expression. tan(60)times3sin(90)-sin(315)

Determine the exact value of expression. tan(60)times3sin(90)-sin(315)

Question
Trigonometry
asked 2020-12-25
Determine the exact value of expression.
\(\displaystyle{\tan{{\left({60}\right)}}}\times{3}{\sin{{\left({90}\right)}}}-{\sin{{\left({315}\right)}}}\)

Answers (1)

2020-12-26
Given,
\(\displaystyle{\tan{{\left({60}\right)}}}\times{3}{\sin{{\left({90}\right)}}}-{\sin{{\left({315}\right)}}}\)
Now, \(\displaystyle{\tan{{\left({60}\right)}}}\times{3}{\sin{{\left({90}\right)}}}-{\sin{{\left({315}\right)}}}\)
\(\displaystyle\sqrt{{{3}}}\times{3}{\left({1}\right)}-{\sin{{\left({360}-{45}\right)}}}\)
\(\displaystyle={3}\sqrt{{{3}}}+{\left(-{\sin{{\left({45}\right)}}}\right)}\)
\(\displaystyle={3}\sqrt{{{3}}}+{\frac{{{1}}}{{\sqrt{{{2}}}}}}\)
\(\displaystyle={\frac{{{3}\sqrt{{{3}}}\times\sqrt{{{2}}}+{1}}}{{\sqrt{{{2}}}}}}\)
\(\displaystyle={\frac{{{3}\sqrt{{{6}}}+{1}}}{{\sqrt{{{2}}}}}}\)
\(\displaystyle={\frac{{{3}\sqrt{{{6}}}+{1}}}{{\sqrt{{{2}}}}}}\times{\frac{{\sqrt{{{2}}}}}{{\sqrt{{{2}}}}}}\)
\(\displaystyle={\frac{{{6}\sqrt{{{3}}}+\sqrt{{{2}}}}}{{{2}}}}\)
0

Relevant Questions

asked 2021-02-05
Determine the exact value of expression.
\(\displaystyle{\tan{{\left({330}\right)}}}\times{\cos{{\left({240}\right)}}}-{2}{\cos{{\left({270}\right)}}}\)
asked 2020-10-18
Determine the exact value of expression.
\(\displaystyle{\sec{{\left({210}\right)}}}\times{\cot{{\left({300}\right)}}}+{\sin{{\left({225}\right)}}}\)
asked 2021-01-04


\(\sec \theta = -3, \tan \theta > 0\). Find the exact value of the remaining trigonometric functions of
\(\theta\).

asked 2021-02-09
The angle \(\displaystyle\theta\) is in the fourth quadrant and \(\displaystyle{\cos{\theta}}={\frac{{{2}}}{{{7}}}}\). Find the exact value of the remaining five trigonometric functions.
asked 2021-03-26
A box weighing 70 N rests on a table. A rope tied to the box runs vertically upward over a pulley and a weight is hung from the other end. Determine the force that the table exerts on the box if the weight hanging on the other side of the pulley weighs a) 30 N b) 60 N and c) 90 N
asked 2021-01-04
Find the linear equations that can be used to convert an (x, y) equation to a (x, v) equation using the given angle of rotation \(\displaystyle{d}{i}{s}{p}{l}{a}{y}{s}{t}{y}\le\theta\).
\(\displaystyle{d}{i}{s}{p}{l}{a}{y}{s}{t}{y}\le\theta={\left\lbrace{\left\lbrace{\tan}\right\rbrace}^{{{\left\lbrace-{\left\lbrace{1}\right\rbrace}\right\rbrace}}}{\left\lbrace{\left({\left\lbrace{5}\right\rbrace}\text{/}{\left\lbrace{12}\right\rbrace}\right)}\right\rbrace}\right\rbrace}\)
asked 2021-02-08
Explain how we can evaluate the expression \(\displaystyle{\cos{{\left({\arctan{{\left({\frac{{{v}}}{{{a}}}}\right)}}}\right)}}}\) and what the evaluation is in terms of v and a.
asked 2020-10-25
Evaluate the following.
\(\displaystyle\int{\frac{{{{\cos}^{{5}}{\left({3}{z}\right)}}{\left.{d}{z}\right.}}}{{{{\sin}^{{2}}{\left({3}{z}\right)}}}}}\)
asked 2020-12-25
Find the value of each trigonometric ratio to the nearest ten-thousandth
\(\displaystyle{{\tan{{50}}}^{\circ}}\)
asked 2021-02-09
Trigonometry is one of the most interesting chapters of Quantitative Aptitude section. Basically, it is a part of SSC syllabus. Today I will tell you the easy method to learn all the basics of trigonometry i.e. Trigonometric Ratios, facts and formulas.
...