حساب المثلثات | Trigonometry — مقرر جامعي مجاني
مِسبار · مقرر جامعي مجاني
Trigonometry

تعلم حساب المثلثات (Trigonometry) مجانًا عبر 4 وحدات و82 فيديو تعليميًا، بإجمالي نحو 10 ساعة، ضمن مكتبة مِسبار الجامعية.
Explore the world of trigonometry by mastering right triangles and their applications, understanding and graphing trig functions, solving problems involving non-right triangles, and unlocking the power of trigonometric equations and identities. This course builds foundational skills and real-world problem-solving techniques essential for advanced math and science studies.
- 4 وحدات.
- 82 فيديو.
- نحو 10 ساعة مشاهدة.
- المستوى: foundation.
ابدأ مشاهدة المقرر داخل مكتبة مِسبار
التخصصات المرتبطة بالمقرر
- الهندسة الكهربائية (Electrical Engineering)
- هندسة الحاسوب (Computer Engineering)
- الهندسة الميكانيكية (Mechanical Engineering)
- الهندسة المدنية (Civil Engineering)
- الهندسة الكيميائية (Chemical Engineering)
- الهندسة الصناعية (Industrial Engineering)
- هندسة الطيران والفضاء (Aerospace Engineering)
- الذكاء الاصطناعي (Artificial Intelligence)
- علم البيانات (Data Science)
- الروبوتات (Robotics)
- الرياضيات (Mathematics)
- الفيزياء (Physics)
- الفلك وعلوم الفضاء (Astronomy & Space Science)
- العمارة (Architecture)
- التصميم الداخلي (Interior Design)
- التخطيط العمراني (Urban Planning)
- تعليم الرياضيات (Mathematics Education)
وحدات ودروس المقرر
1. Right triangles & trigonometry
13 فيديو تعليمي.
موضوعات ودروس الوحدة
- Using similarity to estimate ratio between side lengths
- Using right triangle ratios to approximate angle measure
- Triangle similarity & the trigonometric ratios
- Trigonometric ratios in right triangles
- Solving for a side in right triangles with trigonometry
- Intro to the Pythagorean trig identity
- Sine & cosine of complementary angles
- Using complementary angles
- Trig word problem: complementary angles
- Trig challenge problem: trig values & side ratios
- Right triangle word problem
- Finding reciprocal trig ratios
- Using reciprocal trig ratios
2. Trigonometric functions
31 فيديو تعليمي.
موضوعات ودروس الوحدة
- Unit circle
- The trig functions & right triangle trig ratios
- Intro to radians
- Radians & degrees
- Degrees to radians
- Radians to degrees
- Radian angles & quadrants
- Proof of the Pythagorean trig identity
- Using the Pythagorean trig identity
- Cosine, sine and tangent of π/6 and π/3
- Trig values of π/4
- Sine & cosine identities: symmetry
- Tangent identities: symmetry
- Sine & cosine identities: periodicity
- Tangent identities: periodicity
- Graph of y=sin(x)
- Intersection points of y=sin(x) and y=cos(x)
- Graph of y=tan(x)
- Features of sinusoidal functions
- Transforming sinusoidal graphs: vertical stretch & horizontal reflection
- Transforming sinusoidal graphs: vertical & horizontal stretches
- Amplitude & period of sinusoidal functions from equation
- Example: Graphing y=3⋅sin(½⋅x)-2
- Example: Graphing y=-cos(π⋅x)+1.5
- Sinusoidal function from graph
- Interpreting trigonometric graphs in context
- Trig word problem: modeling daily temperature
- Trig word problem: modeling annual temperature
- Trig word problem: length of day (phase shift)
- Tau versus pi
- Pi is (still) wrong
3. Non-right triangles & trigonometry
7 فيديو تعليمي.
4. Trigonometric equations and identities
31 فيديو تعليمي.
موضوعات ودروس الوحدة
- Intro to arcsine
- Intro to arctangent
- Intro to arccosine
- Restricting domains of functions to make them invertible
- Domain & range of inverse tangent function
- Using inverse trig functions with a calculator
- Solving sinusoidal equations of the form sin(x)=d
- Cosine equation algebraic solution set
- Cosine equation solution set in an interval
- Sine equation algebraic solution set
- Solving cos(θ)=1 and cos(θ)=-1
- Interpreting solutions of trigonometric equations
- Trig word problem: solving for temperature
- Trig angle addition identities
- Using the cosine angle addition identity
- Using the cosine double-angle identity
- Proof of the sine angle addition identity
- Proof of the cosine angle addition identity
- Proof of the tangent angle sum and difference identities
- Finding trig values using angle addition identities
- Using the tangent angle addition identity
- Using trig angle addition identities: finding side lengths
- Using trig angle addition identities: manipulating expressions
- Using trigonometric identities
- Trig challenge problem: area of a triangle
- Trig challenge problem: area of a hexagon
- Trig challenge problem: cosine of angle-sum
- Trig challenge problem: arithmetic progression
- Trig challenge problem: maximum value
- Trig challenge problem: multiple constraints
- Trig challenge problem: system of equations
مقررات مرتبطة
- ما قبل التفاضل والتكامل | Precalculus
- الإحصاء والاحتمالات | Statistics & probability
- التفاضل والتكامل AP (AB) | AP®︎ Calculus AB
- التفاضل والتكامل AP (BC) | AP®︎ Calculus BC
- الإحصاء AP | AP®︎ Statistics
- التفاضل والتكامل متعدد المتغيرات | Multivariable calculus
المصدر والحقوق
المحتوى الأصلي المرخص: أكاديمية خان. تقوم مِسبار بالفهرسة والتنظيم حسب التخصص، وتعرض الفيديوهات المرخصة غير التجارية داخل مكتبة مجانية مستقلة.