Trigonometry : 11th grade math worksheets with answers in PDF

11th grade math worksheets Report an error on this Mathovore page.Report an error / Note? 11th grade
Math worksheets  in 11th grade on metric relations in any triangle.

Exercise 1 – Trigonometric equations
Solve in %5D-\pi;\pi%5D the following equations.
1. cosx=\frac{\sqrt{2}}{2}.
2. sinx=-\frac{\sqrt{3}}{2}.

Exercise 2 – Determine the value of cosine
In this exercise, we give:
Calculate the exact value of cos(\frac{2\pi}{5}) and then of cos(\frac{3\pi}{5}).

Exercise 3 – Exercise on the tangent
In this exercise, we have the following data: tan(\frac{\pi}{12})=2-\sqrt{3}.
1. Let x\in%5D0;\frac{\pi}{2}%5B. Prove that tan(\frac{\pi}{2}-x)=\frac{1}{tanx}.
2. Deduce that :

Exercise 4 – Solving a trigonometric equation
Solve in%5D-\pi;\pi%5D the equation: sin(2x) = cos(x).

Exercise 5 – Solving two trigonometric equations
Solve in%5D-\pi;\pi%5B the following equations:

Exercise 6 – Solving a complex trigonometric equation
Solve in\mathbb{R} the equation :

Exercise 7 – Equilateral triangle and angle measurement
In the figure below, ABC is equilateral, BCI and ACJ are isosceles rectangles at B and J respectively.
Equilateral triangle and angle measurement
1. Determine a measure of each of the following angles:
2. Show that the points A, I and J are aligned.

Exercise 8 – Trigonometric circle and points
Draw a trigonometric circle and place on this circle
the points A, M, N, P and Q marked by the following numbers :

Exercise 9 – Principal measure of an angle
Determine the principal measure of angles:
\alpha\,=\frac{114\pi}{4} ; \beta\,=-\frac{91\pi}{6}; \gamma\,=70

Exercise 10 – Metric relations in the triangle
ABC is a triangle with BC=4,\widehat{B}=\frac{\pi}{4};\widehat{C}=\frac{\pi}{3}.
1. Prove that sin\,\,\,\widehat{A}=\frac{\sqrt{6}+\sqrt{2}}{4}.
2. Calculate the exact values of AB and AC .

Exercise 11 – Graphical representation of trigonometric functions
Show that the graphical representation of the functionf defined on \mathbb{R} by :
is located between the lines of equation y = – 3 and y = 1 .

Exercise 12 – Solving a trigonometric equation
Show that, for any real x:

Exercise 13 – Using addition formulas
Using the addition formulas, calculate the exact value of sin(\frac{7\pi}{12})\,et\,cos(\frac{7\pi}{12}).

Exercise 14 – The Al-Kashi formulas
Let ABC be any triangle.
We note:
– has the length of the segment [BC];
– b the length of the segment [AC];
– c the length of the segment [AB];
The formulas of Al-Kashi
Show that :
a^2=b^2+c^2-2bc\times  \,cos(\alpha\,)\\b^2=a^2+c^2-2ac\times  \,cos(\beta\,)\\c^2=a^2+b^2-2ab\times  \,cos(\gamma\,)\\

Exercise 15 – Trigonometry formula
Show that:

Exercise 16 – Main measure and figure in the plane
Compute the principal measure of (\vec{DC},\vec{DA}) knowing that :

Main measure and figure in the plan.

Exercise 17 – Metric relations in the triangle

ABC is a triangle with BC = 4, \widehat{B}=\frac{\pi}{4} and \widehat{C}=\frac{\pi}{3}.
1. Prove that sin\widehat{A}=\frac{\sqrt{6}+\sqrt{2}}{4}.
2. Calculate the exact values of AB and AC.
3. Calculate the exact value of the area of ABC.

Exercise 18
A triangle ABC has area S = 5 cm².
Moreover, c=AB=13 cm and b=AC= 2 cm.
Calculate the possible length(s) of the third side a = BC.

Exercise 19
ABC is a triangle.
We know that AB = 7, AC= 4 and \widehat{A}=60^{\circ}.
1. Calculate the exact value of BC.
2. Calculate the exact value of sin\widehat{B}.

Exercise 20
Show that two supplementary angles have the same sine.
ABCD is a quadrilateral.We assume that the segments [AC] and [BD] are inside the quadrilateral.
Show that the area S of quadrilateral ABCD is given by :
S=\frac{1}{2}\,\times  \,AC\,\times  \,BD\,\times  \,sin\Theta ( \Theta is the angle formed by the diagonals).

Exercise 21
A walker walks 5 km east, then 2 km northeast, surprised by the weather, he runs straight back to his starting point.
What distance did he run?
We will give the exact value and then the approximate value to the nearest 0.01 km.
Metric relationships

Exercise 22
Prove the following property:
ABC is a right-angled triangle in A \Leftrightarrow sin^2A=sin^2B+sin^2C.

Corrected math exercises.

Cette publication est également disponible en : Français (French) Español (Spanish) العربية (Arabic)

Download and print this document in PDF for free

You have the possibility to download then print this document for free «trigonometry : 11th grade math worksheets with answers in PDF» in PDF format.

Other documents in the category 11th grade math worksheets

Download our free apps with all corrected lessons and exercises.

Application Mathovore sur Google Play Store.    Application Mathovore sur Apple Store.     Suivez-nous sur YouTube.

Other forms similar to trigonometry : 11th grade math worksheets with answers in PDF.

  • 98
    Equations and inequations of the second degree : 11th grade math worksheets with answers in PDF Second degree equations and inequations with online 11th grade math worksheets  to progress in high school math. Exercise #1: Determine the canonical form of the following polynomials: a. b. c. d. e. Exercise 2: Solve the following equations in . a. b. c. d. e. f. g. h. i. Exercise…
  • 98
    Square root : 10th grade math worksheets with answers in PDF Math worksheets on square roots in 11th grade of high school in order to assimilate all the properties of the square root and its definition. This list of sheets is accompanied by detailed answers to practice and review online in preparation for a test. You can also download in PDF…
  • 98
    Arithmetic : 9th grade math worksheets with answers Arithmetic and prime numbers in 9th grade, worksheets with answers to download in PDF in 9th grade. We will learn about the notions of divisor and multiple as well as prime numbers and the decomposition of a whole number into prime factors. Then exercises on irreducible fractions. Exercise 1: Euclidean…

Les dernières fiches mises à jour.

Voici les dernières ressources similaires à trigonometry : 11th grade math worksheets with answers in PDF mis à jour sur Mathovore (des cours, exercices, des contrôles et autres), rédigées par notre équipe d'enseignants.

  1. Abonnements
  2. Maths : cours et exercices corrigés à télécharger en PDF.
  3. Subscriptions
  4. Suscripciones
  5. الاشتراكات

Free registration at Mathovore.  On Mathovore, there is 13 703 978 math lessons and exercises downloaded in PDF.