# Precalculus: trigonometry questions and answers

Recent questions in Trigonometry
Trent Carpenter 2021-08-20 Answered

### If $$\displaystyle{\tan{{x}}}={\frac{{{b}}}{{{a}}}}$$, then find the value of $$\displaystyle\sqrt{{{\frac{{{a}+{b}}}{{{a}-{b}}}}}}+\sqrt{{{\frac{{{a}-{b}}}{{{a}+{b}}}}}}$$

Suman Cole 2021-08-20 Answered

### Prove that $$\displaystyle{2}{\arcsin{{\left({x}\right)}}}={\arccos{{\left({1}-{2}{x}^{{2}}\right)}}}$$ for $$\displaystyle{x}\in{\left({0},{1}\right)}$$

Chardonnay Felix 2021-08-20 Answered

### Verify identify $$\displaystyle{\csc{{\left({x}\right)}}}{\sin{{\left({2}{x}\right)}}}{{\sec}^{{2}}{\left({x}\right)}}={\frac{{{2}}}{{{\cos{{\left({x}\right)}}}}}}$$

Chaya Galloway 2021-08-20 Answered

### Find all solution of the equation in the interval $$\displaystyle{\left[{0},{2}\pi\right]}$$. $$\displaystyle{\left({\cos{{x}}}-{1}\right)}{\left({\sin{{x}}}+{1}\right)}={0}$$

Braxton Pugh 2021-08-20 Answered

### Express $$\displaystyle{{\sin{{67}}}^{\circ}+}{{\cos{{75}}}^{\circ}}$$ in terms of trigonometry ratios of angles between $$\displaystyle{0}^{\circ}$$ and $$\displaystyle{45}^{\circ}$$

Kyran Hudson 2021-08-20 Answered

### If $$\displaystyle{\sin{{x}}}={\frac{{{1}}}{{{3}}}},$$ x in quadrant 1, then find $$\displaystyle{\sin{{\left({2}{x}\right)}}},{\cos{{\left({2}{x}\right)}}},{\tan{{\left({2}{x}\right)}}}$$

Cem Hayes 2021-08-19 Answered

### Simplify the following: $$\displaystyle{\sec{{\left({x}\right)}}}{\csc{{\left({x}\right)}}}{\cos{{\left({x}\right)}}}$$

Lewis Harvey 2021-08-18 Answered

### Find $$\displaystyle\theta$$, if $$\displaystyle-{360}^{\circ}{<}\theta{<}{0}^{\circ}$$ and $$\displaystyle{\cos{{\left(\theta\right)}}}=-{\frac{{\sqrt{{{3}}}}}{{{2}}}}$$ and $$\displaystyle\theta$$ in Quadrant 3.

Annette Arroyo 2021-08-18 Answered

### Simplify the trigonometric expression. $$\displaystyle{\frac{{{\sin{{\left({x}\right)}}}}}{{{\csc{{\left({x}\right)}}}+{\cot{{\left({x}\right)}}}}}}$$

Annette Arroyo 2021-08-18 Answered

### It is given that the smallest positive value of x satisfying $$\displaystyle{3}{\sin{{2}}}{x}={\tan{{x}}}$$ is $$\displaystyle{x}=\theta$$ radians. Select all the other solutions of the equation $$\displaystyle{3}{\sin{{2}}}{x}={\tan{{x}}}$$ for $$\displaystyle{0}{<}{x}{<}{2}\pi$$

Annette Arroyo 2021-08-17 Answered