Solving Trigonometry Problems: Basic, Advanced & Examples

High School
Geometry
Trigonometry

The area of a right triangle is $17.5 c m^{2}$ . One leg is 2cm shorter than the other. Find the length of the shortest side.The length of the shortest side is cm?

Expositur3e 2022-08-31

Use the opposite angle or periodicity identities to answer.
$\frac{\tan (\frac{11 π}{4}) \cos (\frac{19 π}{6})}{\sin (\frac{31 π}{3})}$

Soren Wright 2022-08-22

How to prove these identities are true?
1) $\sin (2 θ) = 2 \sin (θ) \cos (θ)$
2) $\cos (2 θ) = \cos^{2} θ - \sin^{2} θ = 1 - 2 \sin^{2} θ = 2 \cos^{2} θ - 1$
3) $\tan 2 θ = \frac{2 \tan θ}{1 - \tan^{2} θ}$

Braeden Valenzuela 2022-08-20

ABC is an inscribed triangle and chord AD bisects angle A and cuts BC at P. Prove: $\frac{A D}{C D} = \frac{A C}{P C}$ .
GIven: Inscribed $△ A B C$ , chord AD bisects $∠ A and c u t s B C$ at P; chord CD
Prove: $\frac{A D}{C D} = \frac{A C}{P C}$ .
Statements
1.(see above)
2. $∠ D = ∠ D$
3.
4. $∠ B C D = ∠ D A B$
5.
6. $△ A C D - △ C P D$
7. $\frac{A D}{C D} = \frac{A C}{P C}$
Reasons
1.Given
2.
3.Defintion of angle bisectors
4.
5.Substitution
6.
7.

dammeym 2022-08-20

Evaluate the trigonometric function using its period as an aid. $\cos (- 13 \frac{π}{3})$

nascarchic839e9 2022-08-20

In which of the following cases must the Law of Cosines be used to solve a triangle? ASA SSS SAS SSA

Johan Patton 2022-08-20

Rewrite each angle in radian measure as a multiple of $π$ (Do not use a calculator.) $120^{\circ}$

Anito49 2022-08-20

Use half-angle identities to find an exact value without a calculator.
${\cos 75}^{\circ}$

hercegvm 2022-08-20

Triangles ABC and XYZ are shown in the coordinate plane below.
Are triangles ABC and XYZ similar? (Justify your answer using one or more transformations.)

Tamara Anthony 2022-08-20

Prove that two isosceles triangles are similar if any angle of one equals the corresponding angle of the other.
a. Case 1: Equal Vertex Angles
Given: Isosceles $∆ A B C$ , isosceles $∆ D E F, A C = B C, D F = E F, ∠ C = ∠ F$
Prove: $△ A B C \sim △ D E F$
Statementc
1.(see above)
2.
3. $△ A B C \sim △ D E F$
Reasons
1.Given
2. Isosceles triangles with equal vertex angles have equal base angles also.(ex. 2.14 #5)
3. ?

Brugolino7t 2022-08-20

Which pair of angles has congruent values for the ${\sin x}^{\circ}$ and the ${\cos y}^{\circ}$ ?
a. $35^{\circ}; 55^{\circ}$
b. $35^{\circ}; 145^{\circ}$
c. $35^{\circ}; 70^{\circ}$
d. $35^{\circ}; 35^{\circ}$

traquealwm 2022-08-18

Solve equations $0 \leq θ < 2 π$
a) $4 \sqrt{3} = 6 \cos θ$
b) $- 2 + \cos θ = \frac{- 4 - \sqrt{2}}{2}$
c) $- 4 = 4 \cos θ$
d) $- 2 = - 4 \sin θ$

Zaiden Soto 2022-08-18

Find, correct to the nearest degree, the three angles of the triangle with the given vertices.
$A (1, 0, - 1), B (4, - 3, 0), C (1, 5, 5)$
$∠ C A B = ?^{\circ}$
$∠ A B C = ?^{\circ}$
$∠ B C F = ?^{\circ}$
$∠ C A B = ?$
$∠ A B C = ?$
$∠ B C A = ?$

sponsorjewk 2022-08-18

Prove that if a line is drawn parallel to the base of a triangle, it cuts off a triangle similar to the given triangle.

Given: $△ A B C, D E ∣ ∣ A B$
Prove: $△ D E C \sim △ A B C$
PSK $\begin{array}{cc} S t a t e m e n t s & R e a s o n s \\ 1. (s e e a b o v e) & 1. G i v e n \\ 2. & 2. If two parallel lines are cut by a transversal, then the corresponding angles are equal \\ 3. △ D E C \sim △ A B C & 3. \end{array}$

aftredingzo 2022-08-18

The sum of the perimeters of an equilateral triangle and a square is 10. Find the dimensions of the triangle and the square that produce a minimum total area.

torfuqx 2022-08-18

Look at the triangulation of convex polygons again. Prove following statements:
Any triangulation of a convex n-polygon subdivides it into $n - 2$ triangles.
For example, every triangulation of a convex pentagon has $5 - 2 = 3$ triangles, and every triangulation of a hexagon has $6 - 2 = 4$ triangles

Eisregiony1 2022-08-18

We can use identities to help us solve trigonometric equations.
Using a Pythagorean identity we see that the equation
$\sin (x) + \sin^{2} (x) + \cos^{2} (x) = 1$ is equivalent to the basic equation _ whose solutions are x = for any integer k.

boske9s 2022-08-18

Topic: Trigonometric Identities Competencies: determine whether an equation is an identity or a conditional equation, apply trigonometric identities to find other trigonometric values, and solve situational problems involving trigonometric identities
$If \cos x = \frac{4}{5} and \frac{3 π}{2} \leq x \leq 2 π, what is \tan 2 x ?$

Finley Mcintosh 2022-08-18

Use a half-angel formula to find the exact value of $\sin \frac{5 π}{8}$

roletatx 2022-08-18

1. Which of the following statement is true?
a. Triangles and quadrilaterals are both polygons.
b. Triangles and quadrilaterals are both a closed plane figure
c. All A and B is true
2. Which of the following statements present the relation of triangles and quadrilaterals?
a. if you divide a quadrilateral diagonally, you will have two triangles.
b. if you divide a quadrilateral diagonally, you will have three triangles.
c. If you divide a quadrilateral diagonally, you will have four triangles.

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Trigonometry

Trigonometry Problems - Basics, Advanced & Examples