# High school trigonometry questions and answers

Recent questions in Trigonometry
Trigonometric Functions

### Write the trigonometric expression as an algebraic expression. $$\displaystyle{\cos{{\left({\arcsin{{x}}}−{\arctan{{2}}}{x}\right)}}}$$

Trigonometric equation and identitie

### Verify the identity $$\displaystyle{\left({7}{\cos{{x}}}-{\sin{{x}}}\right)}^{{2}}+{\left({\cos{{x}}}+{7}{\sin{{x}}}\right)}^{{2}}={50}$$

Trigonometric equation and identitie

### Verify the identity $$\displaystyle{\sec{\theta}}{\cot{\theta}}-{\sin{\theta}}={\frac{{{{\cos}^{{2}}\theta}}}{{{\sin{\theta}}}}}$$

Trigonometric Functions

### $$\displaystyle{\sec{{2}}}{x}-{1}={0}{\left[{0},{2}\pi\right)}$$ solve for x

Trigonometric equation and identitie

### Prove that $$\displaystyle{{\sin}^{{2}}{\left({\frac{{\pi}}{{{8}}}}+{\frac{{{x}}}{{{2}}}}\right)}}-{{\sin}^{{2}}{\left({\frac{{\pi}}{{{8}}}}-{\frac{{{x}}}{{{2}}}}\right)}}={\frac{{{1}}}{{\sqrt{{{2}}}}}}{\sin{{x}}}$$

Trigonometric equation and identitie

### Verify the identity: $$\displaystyle{\frac{{{\left({\cot{{\left(\theta\right)}}}+{1}\right)}{\left({\cot{{\left(\theta\right)}}}+{1}\right)}}}{{{\csc{\theta}}}}}={\csc{{\left(\theta\right)}}}+{2}{\cos{{\left(\theta\right)}}}$$

Trigonometric equation and identitie

### Verify the identity. $$\displaystyle{{\sin}^{{2}}{\frac{{{t}}}{{{2}}}}}={\frac{{{\tan{{t}}}-{\sin{{t}}}}}{{{2}{\tan{{t}}}}}}$$

Trigonometric Functions

### Use an Addition or Subtraction Formula to write the expression as a trigonometric function of one number, and then find its exact value. $$\displaystyle{\left({\cos}\right)}\frac{{{13}\pi}}{{15}}{\cos{{\left(-\frac{\pi}{{5}}\right)}}}-{\left({\sin}\right)}\frac{{{13}\pi}}{{15}}{\sin{{\left(-\frac{\pi}{{5}}\right)}}}$$

Non-right triangles and trigonometry

### What is the value of the following expression: $$\displaystyle\sqrt{{3}}{{\cot{{15}}}^{\circ}}$$

Non-right triangles and trigonometry

### Find the length of the third side of the right triangle, if one side = $$\displaystyle{4}\sqrt{{3}}$$, and the hypotenuse = $$8$$.

Trigonometric Functions

### Select the point on the terminal side of 0. $$\displaystyle{0}=-{60}°$$ (a) $$\displaystyle{\left(-{1},-{1}\right)}$$ (b) $$\displaystyle{\left({1},-√{3}\right)}$$ (c) $$\displaystyle{\left(-√{3},{1}\right)}$$

Non-right triangles and trigonometry

### Suppose that you are headed toward a plateau 50 meters high. If the angle of elevation to the top of the plateau is 60°, how far are you from the base of the plateau?

Non-right triangles and trigonometry

### Given a right triangle. anglea is $$\displaystyle{51}^{\circ}$$. A line is drawn from anglec $$\displaystyle{\left({90}^{\circ}\right)}$$ to the hypotenuse, creating a $$\displaystyle{7}^{\circ}$$ angle between the line and the cathetus adjusted to angleb. The cathetus adjusted to angel is 47cm. Find the length of the line drawn.

Trigonometric equation and identitie

### Verify the identify. $$\displaystyle{\frac{{{{\tan}^{{2}}\theta}}}{{{\sec{\theta}}+{1}}}}={\frac{{{1}-{\cos{{x}}}}}{{{\cos{{x}}}}}}$$

Trigonometric equation and identitie

### Proof trigonometric identities. $$\displaystyle{\sec{{\left({x}\right)}}}+{\tan{{\left({x}\right)}}}={\frac{{{\cos{{\left({x}\right)}}}}}{{{1}-{\sin{{\left({x}\right)}}}}}}$$

Trigonometric equation and identitie

### Establish identity $$\displaystyle{\frac{{{1}+{\tan{{v}}}}}{{{1}-{\tan{{v}}}}}}={\frac{{{\cot{{v}}}+{1}}}{{{\cot{{v}}}-{1}}}}$$

Trigonometric equation and identitie

### Solve the following equation for all radian solutions and if $$\displaystyle{0}\leq{x}\leq{2}\pi$$. Give all answers as exact values in radians. $$\displaystyle{0}\leq{x}\leq{2}\pi$$ $$\displaystyle{x}={\frac{{{7}\pi}}{{{6}}}},{\frac{{\pi}}{{{2}}}},{\frac{{{11}\pi}}{{{6}}}}\ {r}{a}{d}$$

Trigonometric Functions

### evaluate the function for the indicated values. $$\displaystyle{f{{\left({x}\right)}}}={\left[{x}\right]}.{f{{\left({2.1}\right)}}}$$

Trigonometric equation and identitie

### Prove the identity $$\displaystyle{\frac{{{\sin{{\left({2}{x}\right)}}}}}{{{\sin{{\left({x}\right)}}}}}}-{\frac{{{\cos{{\left({2}{x}\right)}}}}}{{{\cos{{\left({x}\right)}}}}}}={\sec{{\left({x}\right)}}}$$

Trigonometric equation and identitie