Trigonometry

Right-angled triangles first, then the sine and cosine rules that handle every other triangle — plus bearings, three-dimensional problems and the trigonometric graphs.

หลักสูตรแกนกลาง / สสวท.: การวัดและเรขาคณิต (Geometry and Measure)ครอบคลุม ม.2 บทที่ 1 พีทาโกรัส · ม.4 อัตราส่วนตรีโกณมิติ · ม.5 ฟังก์ชันตรีโกณมิติ
Common Core (US): G-SRT, F-TF
Cambridge: IGCSE 0580 — Topic 6: Trigonometry (Core and Extended)

9.1 Right-angled triangles

Pythagoras and the three ratios

a^{2} + b^{2} = c^{2} sin θ = \frac{O}{H} cos θ = \frac{A}{H} tan θ = \frac{O}{A}

Mark the angle FIRST, then label the sides relative to it. Opposite and adjacent are not properties of the triangle.

Choosing what to use

1Three sides involved and no angle: Pythagoras
2Two sides and an angle: pick the ratio containing the side you know and the one you want
3Finding an angle: the same ratio, used inversely
4Check the answer against the picture before writing it down

ตัวอย่าง

A ramp rises $1.2$ m over a slope length of $7.5$ m. Find the angle with the horizontal.

วิธีทำ

1.Opposite $1.2$ , hypotenuse $7.5$ — so sine
2. $sin θ = \frac{1.2}{7.5} = 0.16$
3. $θ = sin^{- 1} (0.16)$

ตอบ $9. 2^{\circ}$ (1 d.p.)

ข้อควรระวัง

Set the calculator to DEGREES. A radian-mode answer is an ordinary-looking number with nothing on the page to suggest it is wrong, which is what makes this the most costly setting on the device.

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