Asked by FaithMaths 💯

Trigonometry - how do you find the special angles (sin 30,45,60; cos 30,45,60 and tan 30,45,60)?

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Sohini Khan

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The best way (without using a calculator) is by memorising the two triangles: 1. an isosceles right-angled triangle with lengths 1, 1 and 2 (hypotenuse) and angles 45°, 45° and 90° 2. a right-angled triangle with lengths 1, rt3 and 2 (hypotenuse) and angles 30°, 60° and 90° - the 30° angle should be opposite the side of length 1 as it’s the smallest angle If you memorise these two triangles, and know SOHCAHTOA, you can find any of the special angles listed in your question. For example, for cos30, I would look at the second triangle and find the adjacent side (rt3) and the hypotenuse (2) to the 30° angle. This means cos30 = rt3/2 (CAH). Alternatively, for tan45, I would look at the first triangle and find the opposite side (1) and the adjacent side (1) to the 45° angle. This means tan45 = 1/1 = 1 (TOA). Hope that’s clear - a little difficult to describe triangles without images! Sohini

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