Trigonometry & Heights / Distances • Topic 1 of 4

Trigonometric Ratios

In a right triangle, for an acute angle: sine = opposite/hypotenuse, cosine = adjacent/hypotenuse, tangent = opposite/adjacent. The reciprocals are cosecant, secant and cotangent. Given one ratio you can reconstruct the triangle (using Pythagoras) and read off the others — for example, if sin = 3/5, the sides are 3, 4, 5 and cos = 4/5, tan = 3/4.

✅ Solved examples

1. If sin A = 3/5, find cos A and tan A.
Sides 3,4,5: cos A = 4/5, tan A = 3/4.
2. If tan A = 1, what is angle A (acute)?
tan 45 = 1, so A = 45 degrees.
3. If cos A = 12/13, find sin A.
Sides 5,12,13: sin A = 5/13.
4. Value of sin 30 + cos 60?
1/2 + 1/2 = 1.

✏️ Practice — try these, take hints as needed

1. sin A = 8/17 -> cos A?
Triple 8,15,17.
adjacent 15.
—
15/17
2. tan A = root 3 -> A?
Standard angle.
—
—
60 degrees
3. cos 0 + sin 90?
Both 1.
—
—
2
4. cos A = 3/5 -> tan A?
Sides 3,4,5; opp 4.
tan = 4/3.
—
4/3
5. sec 60?
1/cos 60.
1/(1/2).
—
2

📝 Topic test — 8 questions

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