Lesson · Grade 10 · Foundations of Mathematics and Pre Calculus
Sine, cosine and tangent: the three trig ratios
- Grade 10
- Foundations of Mathematics and Pre Calculus
- 2 min 13 s
- British Columbia
- BC10-MA-35
Using one 3-4-5 right triangle, the video names the hypotenuse, opposite and adjacent sides from angle A, then uses SOH CAH TOA to work out sin A = 3/5 = 0.6, cos A = 4/5 = 0.8 and tan A = 3/4 = 0.75, and warns against putting the hypotenuse in the tangent ratio. A 6-8-10 triangle with the same angle gives the same three ratios, which shows that each ratio depends only on the angle.
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In one sentence
The question this lesson answers
In a right triangle, three ratios link an angle to the sides: sine, cosine and tangent.
Its right angle, 90 degrees, is marked by the small square.
Transcript
What the lesson says
In a right triangle, three ratios link an angle to the sides: sine, cosine and tangent.
Its right angle, 90 degrees, is marked by the small square.
Its sides are 3, 4 and 5 centimetres, and we study the angle marked A.
The hypotenuse is the longest side, across from the right angle. Here it is 5 centimetres.
The opposite side is across from angle A. Here it is 3 centimetres.
The adjacent side is next to angle A but is not the hypotenuse. Here it is 4 centimetres.
Each ratio is one side divided by another, and SOH CAH TOA tells you which sides.
SOH: the sine of A is opposite over hypotenuse.
In our triangle, that is 3 over 5, which is 0.6.
CAH: the cosine of A is adjacent over hypotenuse.
That is 4 over 5, which is 0.8.
TOA: the tangent of A is opposite over adjacent.
That is 3 over 4, which is 0.75.
A common mistake is putting the hypotenuse in the tangent ratio. Tangent uses only the opposite and adjacent sides.
Now take a bigger triangle with the same angle A and every side doubled: 6, 8 and 10 centimetres.
Sine is 6 over 10, still 0.6. Cosine is 8 over 10, still 0.8. Tangent is 6 over 8, still 0.75.
The triangle changed size, but the ratios did not. Each ratio depends only on the angle.
Recap: SOH CAH TOA. Sine is opposite over hypotenuse, cosine is adjacent over hypotenuse, and tangent is opposite over adjacent.
Curriculum
Where this fits
- British Columbia, Grade 10
Foundations of Mathematics and Pre Calculus 10, Trigonometry: primary trigonometric ratiosBC10-MA-35
Previous: Naming the Sides of a Right Triangle: Hypotenuse, Opposite, AdjacentNext: Finding a missing side with a trig ratio
- British Columbia, Grade 10
Workplace Mathematics 10, Trigonometry: primary trigonometric ratiosBC10-MA-48
Previous: Naming the Sides of a Right Triangle: Hypotenuse, Opposite, AdjacentNext: Finding a missing side with a trig ratio
The outcomes and strands follow the British Columbia curriculum.
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