# Trigonometric equation and identitie Answers Trigonometric equation and identitie ### For a Science fair project, a group of students tested different Materials used to construct kites. The instructor gave to the group an instrument that accurately measures the angle of elevation. In one of the tests, the angle of elevation was 63.4° with 670 ft of string out. Assuming the string was taut, how high was the kite?

Trigonometric equation and identitie ### solve the following equation for all values of x: $$\displaystyle{{\sin}^{{2}}{x}}+{\sin{{x}}}{\cos{{x}}}$$

Trigonometric equation and identitie ### Solve $$(\sin x + \cos x)(\sin x + \cos x)$$

Trigonometric equation and identitie ### Solve $$\displaystyle{{\tan}^{{2}}{x}}-{{\sin}^{{2}}{x}}={{\tan}^{{2}}{x}}{{\sin}^{{2}}{x}}$$

Trigonometric equation and identitie ### Find the exact value of the expression. $$( tan25^(circ) +tan110^(circ))/(1-tan25^(circ)*tan110^(circ))$$

Trigonometric equation and identitie ### Movement of a Pendulum A pendulum swings through an angle of 20∘ each second. If the pendulum is 40 inches long, how far does its tip move each second? Round answers to two decimal places.

Trigonometric equation and identitie ### Solve $$\frac{(\sin \theta+\cos \theta)}{\cos \theta}+\frac{(\sin \theta-\cos \theta)}{\cos \theta}$$

Trigonometric equation and identitie ### How to prove the following: $$\displaystyle{{\tan}^{{2}}{x}}+{1}+{\tan{{x}}}{\sec{{x}}}={1}+\frac{{\sin{{x}}}}{{{\cos}^{{2}}{x}}}$$

Trigonometric equation and identitie ### Prove that $$\displaystyle{\text{sinh}{{\left({x}+{y}\right)}}}={\sin{{x}}}{\text{cosh}{{y}}}+{\text{cosh}{{x}}}{\text{sinh}{{y}}}$$

Trigonometric equation and identitie ### If $$\displaystyle{\cos{{x}}}=-\frac{{12}}{{13}}{\quad\text{and}\quad}{\csc{{x}}}{<}{0}$$, find $$\displaystyle{\cot{{\left({2}{x}\right)}}}$$

Trigonometric equation and identitie ### Find every angle theta with $$\displaystyle{0}\le\theta\le{2}\pi{r}{a}{d}{i}{a}{n}{s},{\quad\text{and}\quad}{2}{{\sin}^{{2}}{\left(\theta\right)}}+{\cos{{\left(\theta\right)}}}={2}$$

Trigonometric equation and identitie ### $$\displaystyle{\cos{{360}}}+{\cos{{234}}}+{\cos{{162}}}+{\cos{{18}}}=$$ ? Note - numbers are in degree.

Trigonometric equation and identitie ### Solve the equation $$\frac{\sin^{2}\theta/}{cos \theta}= \sec \theta-\cos \theta$$

Trigonometric equation and identitie ### Prove that: $$\displaystyle{1}+\frac{{\cos{{x}}}}{{1}}-{\cos{{x}}}=\frac{{{\tan}^{{2}}{x}}}{{\left({\sec{{x}}}-{1}\right)}^{{2}}}$$

Trigonometric equation and identitie ### $$\displaystyle{\left({\cos{{A}}}\right)}{\left({\csc{{A}}}\right)}={\cot{{A}}}$$

Trigonometric equation and identitie ### Multiply and simplify: $$\frac{(\sin \theta+\cos \theta)(\sin \theta+\cos \theta)-1}{\sin \theta \cos \theta}$$

Trigonometric equation and identitie ### Solve the equation \frac{\cot(x)-\tan(x)}{(\cot^{2}(x)-\tan^{2}(x)}=\sin x\cos x

Trigonometric equation and identitie ### [Triangle] Find sin 1),sin #,cos 1), and cos &. Write each answer as a fraction in simplest form.

Trigonometric equation and identitie ### Prove that $$\displaystyle\frac{{{\cos{{A}}}-{\cos{{B}}}}}{{{\sin{{A}}}+{\sin{{B}}}}}=\frac{{{\sin{{B}}}-{\sin{{A}}}}}{{{\cos{{A}}}+{\cos{{B}}}}}$$ 