Trigonometry Problems - Basics, Advanced & Examples

Solve the equation $\csc x-\sin x=\cot x\cos x$

Solve $4({\sin }^{6}x+{\cos }^{6}x)=4-3{\sin }^{2}2x$

Consider the non-triangle below. Suppose that ${\displaystyle \mathrm{\angle }ACB={103}^{\circ }}$ and ${\displaystyle m\mathrm{\angle }BAC={44}^{\circ }}$, and that $y=50.5cm$. What of the value of X?

The length of the base of an isosceles triangle is x. The length of a leg is 2x - 6. The perimeter is 53. Find x.

A garden in the shape of a regular hexagon has sides that are each 5 meters long. If the height of each of the congruent triangles within the hexagon is about 4.33 meters, what is the area of the garden?

The drawing shows a uniform electric field that points in the negative y direction; the magnitude of the field is 5300 N/C.Determine the electric potential difference (a) VB - VA between points A and B, (b) VC - VB between points B and C, and (c) VA - VB between points C and A.
A-C is 10.0cm, b-c is 8.0 cm, a-b is 6.0 cm. They are all in a right triangle shape. With angle b having the 90 degree angle, and electric potential is pointing down. This is problem 56 in 7th edition.

Challenge In $\mathrm{△}ABC,m\mathrm{\angle }B$ is one-third the $m\mathrm{\angle }A\text{and}m\mathrm{\angle }C$ is 37 less than the $m\mathrm{\angle }A.$. What are the measures of the angles of $\mathrm{△}ABC$?

The sides of a triangle are 5.2 cm, 6.3 cm and 9.4 cm, each correct to the nearest millimetre. Calculate the lower bound of the perimeter of the triangle

Given a triangle with all angles equal and sides equal to:
1. $3x-5$
2. $4x-30$
3. $2x+20$
Find the value of x.

What is the path that traces the circle in the plane =1 with radius =5 and center (−7,1,1) with constant speed 15?

Triangle DEF is shown below. What is the measure of ${\displaystyle \angle D}$?

What is ${\displaystyle \theta }$ equal to
1. in radians,
2. in degrees,
if, ${\displaystyle \cot \left(\theta \right)=1}$

PQRS is a parallelogram. ${\displaystyle m\angle Q=11x+13}$ and ${\displaystyle m\angle S=15x-23}$. Find the measure of ${\displaystyle \angle P}$.

Prove that ${\displaystyle \sec \left(\theta \right)+\csc \left(\theta \right)=(\sin \left(\theta \right)+\cos \left(\theta \right))(\tan \left(\theta \right)+\cot \left(\theta \right))}$

Solve $(2\sin x\cot x+\sin x+4\cot x-2)/(2\cot x+1)=\sin x-2$

A necklace comes with a gol square centimeters?

Find the remaining angles for ${\displaystyle △ABC}$. ${\displaystyle m\angle B=30\circ \text{and}m\angle A=\frac{1}{2}m\angle C}$
${\displaystyle m\angle A=\surd \circ }$ and ${\displaystyle m\angle C=\surd \circ }$

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

The sum of two acute angles is an acute angle. always true, never or sometimes. Explain.

In triangle ABC with sides a, b, and c the Law of Sines states that