A7LAM CSCA ACADEMYCSCA Academy / Mathematics / Functions
CSCA Mathematics · Lesson 6 of 16Trigonometry
Trigonométrie · حساب المثلثات
▶ Watch the video lesson (A7LAM students)
Trigonometry connects angles and lengths. Learn the special values by heart: they save a lot of time.
Key ideas
- In a right triangle: sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, tan θ = opposite/adjacent.
- Special values: sin 30° = 1/2, sin 45° = √2/2, sin 60° = √3/2, and cos 60° = 1/2.
- Radians: 180° = π rad.
- Key identity: sin²θ + cos²θ = 1.
Formulas to know
- tan θ = sin θ / cos θ
- sin(2θ) = 2 sin θ cos θ
- Law of sines: a/sin A = b/sin B = c/sin C
Worked example
In a right triangle the hypotenuse is 10 and one angle is 30°. Find the side opposite that angle.
- sin 30° = opposite / hypotenuse.
- 1/2 = opposite / 10.
Answer: opposite = 5
Practice questions
1. cos 60° = ?
1/2 ✓ · √3/2 · √2/2 · 1
A special value: cos 60° = 1/2.
2. Convert 90° to radians.
π · π/2 ✓ · π/3 · 2π
90° = 180°/2 = π/2.
3. If sin θ = 3/5 and θ is acute, cos θ = ?
2/5 · 3/4 · 4/5 ✓ · 5/3
cos²θ = 1 − 9/25 = 16/25, so cos θ = 4/5.