Trigonometry Problems - Basics, Advanced & Examples

Solve ${\displaystyle \sqrt{3}\csc 2x=2}$ for all values of x.

Describe how to identify the vertex angle of an isosceles triangle.

A rectangle with dimensions 21.6 × 12 has a right triangle with a base 9.6 and a height of 7.2 cut out of the rectangle. What is the area of the shaded region?

Expanding isosceles triangle The legs of an isosceles right tri- angle increase in length at a rate of 2 m/s.
a. At what rate is the area of the triangle changing when the legs are 2 m long?
b. At what rate is the area of the triangle changing when the hypot- enuse is 1 m long?
c. At what rate is the length of the hypotenuse changing?

Show that the points form the vertices of the indicated polygon.
Right triangle: A(4, 0), B(2, 1), C(−1, −5)

if ${\displaystyle \mathrm{\angle }c=\mathrm{\angle }b\text{and}\mathrm{\angle }a=4\mathrm{\angle }b}$, find the value of each angle.

Express in terms of sin x: ${\displaystyle \frac{{\cot }^{2}x-1}{{\csc }^{2}x}}$

Geometry -concepts and properties for SSC CGL Tier-I Geometry is one of the most important topics of Quantitative Aptitude section of SSC CGL exam. It includes various concepts related to lines, angles, triangles, circles, polygons and so on. So, today I will just discuss concept and properties of triangle. Always remember that in Geometry, You need a very basic understanding. Cramming is not gonna help you anywhere.

The measure of the complement of an angle is three times the measure of the angle. What is the measure of each angle?

solve the multiple-angle equation. $\tan 3x-1=0$

Calculate the tension ${\displaystyle F_T}$ in the wire that supportsthe 30 kg beam shown in the picture, and the force ${\displaystyle F_W}$ exerted by the wall on the beam (give magnitude and direction.)

Match each of the trigonometric expressions below with the equivalent non-trigonometric function from the following list. Enter the appropriate letter(A,B, C, D or E)in each blank
A . ${\displaystyle \tan \left(\arcsin \left(\frac{x}{8}\right)\right)}$
B . ${\displaystyle \cos \left(ar\sin \left(\frac{x}{8}\right)\right)}$
C. ${\displaystyle \left(\frac{1}{2}\right)\sin \left(2\arcsin \left(\frac{x}{8}\right)\right)}$
D. ${\displaystyle \sin \left(\arctan \left(\frac{x}{8}\right)\right)}$
E. ${\displaystyle \cos \left(\arctan \left(\frac{x}{8}\right)\right)}$

Are triangles necessarily congruent, is:
1. Each side of one triangle is equal to one of the other triangles

[Triangle] Find each x (x+30)∘

Write the trigonometric expression ${\displaystyle \cos ({\sin }^{-1}x-{\cos }^{-1}y)}$ as an algebraic expression (that is, without any trigonometric functions). Assume that x and y are positive and in the domain of the given inverse trigonometric function.

Find the exact value of the trigonometric function ${\displaystyle \sec \left(\frac{-9\pi }{4}\right)}$ .

Find the length of a leg of an isosceles right triangle whose hypotenuse has length 12

Find the exact value of y.

comprehension check for derivatives of trigonometric functions:
a) true or false: if ${\displaystyle fprime\left(\theta \right)=-\sin \left(\theta \right),thenf\left(\theta \right)=\cos \left(\theta \right).}$
b) true or false: ${\displaystyle If\theta }$ is one of the non right angles in a right triangle and $\sin (\theta )=2/3$, then the hypotenuse of the triangle must have length 3.

Solve ${\displaystyle \tan x+\sec 2x=1}$