Recent questions in Trigonometry

Right triangles and trigonometry

Solving Multl-Step Equations (continued)

Right triangles and trigonometry

Tell whether two angles can be as described. Justify your answers. a. vertical and complementary b. vertical and supplementary c. complementary and supplementary

Right triangles and trigonometry

Draw a triangle that satisfies the set of conditions. Then classify the triangle. a triangle with three acute angles and three congruent sides.

Right triangles and trigonometry

Veronica made a triangle by taking an 8 $$1/2 \times; 11$$ sheet of paper and putting a dot at the top. She then drew lines from the bottom corners to the dot and cut along the lines (see diagram). [Triangles] What is the area of the triangle that Veronica cut out?

Trigonometric Functions

$$\displaystyle\frac{{{1}+{\cos{{x}}}}}{{\sin{{x}}}}={\csc{{x}}}+{\cot{{x}}}$$

Trigonometric Functions

The terminal side of an angle $$\theta$$ in standard position intersects the unit circle at $$\displaystyle{\left(\frac{{5}}{{13}},\frac{{12}}{{13}}\right)}$$. What is $$\sin (\theta)$$? Write your answer in simplified, rationalized form.

Trigonometric equation and identitie

Airline passengers arrive randomly and independently at the passenger-screening facility at a major international airport. The mean arrival rate is 11 passengers per minute.

Right triangles and trigonometry

If the hypotenuse of a $$45^{\circ}-45^{\circ}-90^{\circ}$$ triangle has a length of $$\displaystyle\sqrt{2}$$, how long are the legs?

Trigonometric Functions

$$\tan 28^{\circ} = \cot ?$$

Right triangles and trigonometry

In triangle ABC, $$a=15$$, $$b=14$$, $$c=10$$. Find $$\displaystyle{m}{<}{B}$$

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 $$60^{\circ}$$, how far are you from the base of the plateau?

Trigonometric equation and identitie

Prove the identity $$\frac{1}{2\csc 2x}=\cos^2 x \tan x$$ Choose the sequence of steps below that verifies the identity A) $$\cos^2 x \tan x =\cos^2 x \frac{\sin x}{\cos x}=\cos x \sin x =\frac{\sin 2x}{2}=\frac{1}{2\csc 2x}$$ B) $$\cos^2 x \tan x=\cos^2 x \frac{\cos x}{\sin x}=\cos x \sin x=\frac{\sin 2x}{2}=\frac{1}{2 \csc 2x}$$ C) $$\cos^2 x \tan x=\cos^2 x \frac{\cos x}{\sin x}=\cos x \sin x=2 \sin 2x=\frac{1}{2 \csc 2x}$$ D) $$\cos^2 x \tan x =\cos^2 x \frac{\sin x}{\cos x}=\cos x \sin x=2 \sin 2x=\frac{1}{2 \csc 2x}$$

Trigonometric equation and identitie

(1,5 points) Find the intervals of concavity and the inflection points of the function $$\displaystyle{f{{\left({x}\right)}}}={x}{\left({2}{x}−{1}\right)}^{{2}}$$

Trigonometric Functions

$$\displaystyle{\tan{{\left({x}\right)}}}{\sin{{\left({x}\right)}}}+{\sec{{\left({x}\right)}}}{{\cos}^{{2}}{\left({x}\right)}}={\sec{{\left({x}\right)}}}$$

Trigonometric Functions

$$\displaystyle\frac{{\sin{{\left({a}-{b}\right)}}}}{{\cos{{a}}}}{\cos{{b}}}={\tan{{a}}}-{\tan{{b}}}$$

Right triangles and trigonometry

Two college friends are taking a weekend road trip. Friday they leave home and drive 87 miles north for a night of dinner and dancing in the city. The next morning they drive 116 miles east to spend a day at the beach. If they drive straight home from the beach the next day, how far do they have to travel on Sunday?

Trigonometric Functions

If $$A = 40^{\circ}, B = 60^{\circ}$$, and $$a = 20$$, find b.

Right triangles and trigonometry