Trigonometry
sin, cos and tan, the special angles, and identities.
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In a right triangle, the angle decides the shape, so it decides the ratio of the sides.
Look: Opposite faces the angle θ. Adjacent is next to it. Hypotenuse is the longest.
✏️ Your turn!
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1tan 45° = ?
2sin 30° = ?
3cos 60° = ?
! Careful!
✗Naming the sides without looking at the angle.
✓Always name sides from the angle.
✗sin 30° + sin 60° = sin 90°.
✓Trig values do not add like that.
See the whole lesson on one page
In a right triangle, the angle decides the shape, so it decides the ratio of the sides.
Name the sides from the angle: opposite faces it, adjacent is next to it, hypotenuse is the longest. Remember SOH CAH TOA.
Think of it like thisA steeper slide is taller for the same length. sin, cos and tan just measure how steep, using side lengths.
- sin
- Opposite ÷ Hypotenuse (SOH)
- cos
- Adjacent ÷ Hypotenuse (CAH)
- tan
- Opposite ÷ Adjacent (TOA)
Solved together
A right triangle has sides 3, 4 and 5. Find sin A, cos A and tan A.
Find the sides from angle A.
Use SOH CAH TOA.
sin A = 3/5cos A = 4/5tan A = 3/4
Answersin A = 3/5, cos A = 4/5, tan A = 3/4.
For older learners and grown-ups: a little more
Key values: sin 30° = ½, sin 45° = 1/√2, sin 60° = √3/2 (cos is the reverse order). Identity: sin²θ + cos²θ = 1 (Pythagoras on the unit triangle).
Now practise it
Kanakku makes new questions on trigonometry every time. It shows the working and gives a hint when you are stuck.