A lesson about the six trigonometric ratio

1. Trigonometric Ratios
Grade 9 Mathematics | MELCs-
aligned (M9GE-IVa-1)

2. Learning Competencies (MELCs)
• Illustrates the six trigonometric ratios: sine,
cosine, tangent, secant, cosecant, and
cotangent.
– Applies trigonometric ratios to solve right
triangles.
– Finds missing sides and angles of right triangles.

3. What is Trigonometry?
• Trigonometry is a branch of Mathematics that
studies the relationship between angles and
sides of triangles.
– It focuses mainly on right triangles.
– Used to measure heights, distances, and angles.

4. Right Triangle Review
• A right triangle has one angle equal to 90°.
– Hypotenuse – the longest side, opposite the right
angle.
– Opposite side – across the given angle.
– Adjacent side – beside the given angle.

5. Six Trigonometric Ratios
• Sine (sin θ) = Opposite / Hypotenuse
– Cosine (cos θ) = Adjacent / Hypotenuse
– Tangent (tan θ) = Opposite / Adjacent
– Secant (sec θ) = Hypotenuse / Adjacent
– Cosecant (csc θ) = Hypotenuse / Opposite
– Cotangent (cot θ) = Adjacent / Opposite

6. SOH–CAH–TOA
• A mnemonic to remember sine, cosine, and
tangent.
– SOH: Sine = Opposite / Hypotenuse
– CAH: Cosine = Adjacent / Hypotenuse
– TOA: Tangent = Opposite / Adjacent

7. Important Reminder
• Trigonometric ratios depend on the angle, not
the size of the triangle.
– Similar triangles have equal trigonometric ratios.
– Ratios remain constant for a given angle.

8. Sample Problem
• Given: A right triangle with angle θ.
– Opposite side = 5 units, Hypotenuse = 13 units.
– Find sin θ, cos θ, and tan θ.