🌟 Trigonometric Functions – Complete
Study Notes 🌟
1️⃣ What is the sine function in trigonometry?
The sine function (sin) is one of the main trigonometric ratios.
In a right triangle:
sin(θ) = Opposite / Hypotenuse
✅ Example:
If the opposite side = 3 and the hypotenuse = 5,
sin(θ) = = 0.6
2️⃣ Using the cosine function to find an angle
The cosine function (cos) compares the adjacent side to the hypotenuse:
cos(θ) = Adjacent / Hypotenuse
To find the angle:
θ = cos⁻¹(Adjacent / Hypotenuse)
✅ Example:
If the adjacent side = 4 and the hypotenuse = 5,
θ = cos⁻¹() ≈ 36.87°
3️⃣ The tangent function
The tangent (tan) compares the opposite side to the adjacent side:
tan(θ) = Opposite / Adjacent
✅ Example:
If tan(θ) = 0.75, then
θ = tan⁻¹(0.75) ≈ 36.87°
, 4️⃣ Relationship between sine, cosine, and tangent
These three are connected by:
tan(θ) = sin(θ) / cos(θ)
They describe relationships between sides of a right triangle or coordinates on the unit circle.
5️⃣ Using inverse trigonometric functions
Inverse trigonometric functions find the angle from a given ratio:
sin⁻¹, cos⁻¹, tan⁻¹
✅ Example:
If sin(θ) = 0.5, then
θ = sin⁻¹(0.5) = 30°
6️⃣ The cosecant function
The cosecant (csc) is the reciprocal of sine:
csc(θ) = 1 / sin(θ) = Hypotenuse / Opposite
7️⃣ The secant function
The secant (sec) is the reciprocal of cosine:
sec(θ) = 1 / cos(θ) = Hypotenuse / Adjacent
8️⃣ The cotangent function
The cotangent (cot) is the reciprocal of tangent:
cot(θ) = 1 / tan(θ) = Adjacent / Opposite
9️⃣ Using trigonometric identities
Trigonometric identities are always true formulas used to simplify expressions.
Study Notes 🌟
1️⃣ What is the sine function in trigonometry?
The sine function (sin) is one of the main trigonometric ratios.
In a right triangle:
sin(θ) = Opposite / Hypotenuse
✅ Example:
If the opposite side = 3 and the hypotenuse = 5,
sin(θ) = = 0.6
2️⃣ Using the cosine function to find an angle
The cosine function (cos) compares the adjacent side to the hypotenuse:
cos(θ) = Adjacent / Hypotenuse
To find the angle:
θ = cos⁻¹(Adjacent / Hypotenuse)
✅ Example:
If the adjacent side = 4 and the hypotenuse = 5,
θ = cos⁻¹() ≈ 36.87°
3️⃣ The tangent function
The tangent (tan) compares the opposite side to the adjacent side:
tan(θ) = Opposite / Adjacent
✅ Example:
If tan(θ) = 0.75, then
θ = tan⁻¹(0.75) ≈ 36.87°
, 4️⃣ Relationship between sine, cosine, and tangent
These three are connected by:
tan(θ) = sin(θ) / cos(θ)
They describe relationships between sides of a right triangle or coordinates on the unit circle.
5️⃣ Using inverse trigonometric functions
Inverse trigonometric functions find the angle from a given ratio:
sin⁻¹, cos⁻¹, tan⁻¹
✅ Example:
If sin(θ) = 0.5, then
θ = sin⁻¹(0.5) = 30°
6️⃣ The cosecant function
The cosecant (csc) is the reciprocal of sine:
csc(θ) = 1 / sin(θ) = Hypotenuse / Opposite
7️⃣ The secant function
The secant (sec) is the reciprocal of cosine:
sec(θ) = 1 / cos(θ) = Hypotenuse / Adjacent
8️⃣ The cotangent function
The cotangent (cot) is the reciprocal of tangent:
cot(θ) = 1 / tan(θ) = Adjacent / Opposite
9️⃣ Using trigonometric identities
Trigonometric identities are always true formulas used to simplify expressions.
