Математика28 мин

Trigonometry

Sin, cos, tan ratios, the special angles, sine/cosine rules, and the identities you actually need.

SOHCAHTOA

\sin\theta = \dfrac{\text{opp}}{\text{hyp}},\quad \cos\theta = \dfrac{\text{adj}}{\text{hyp}},\quad \tan\theta = \dfrac{\text{opp}}{\text{adj}}

\dfrac{a}{\sin A} = \dfrac{b}{\sin B} = \dfrac{c}{\sin C}

Sine rule.

c^2 = a^2 + b^2 - 2ab\cos C

Cosine rule — generalised Pythagoras.

Use sine rule when you have an angle paired with its opposite side. Use cosine rule for SAS or SSS.

\sin^2\theta + \cos^2\theta = 1

\tan\theta = \dfrac{\sin\theta}{\cos\theta}

Жаттығу

If $\sin\theta = 3/5$ and $\theta$ is acute, find $\cos\theta$ .

Жауап пен түсініктемені көру

Жауап: $4/5$

$\cos^2\theta = 1 - 9/25 = 16/25 \Rightarrow \cos\theta = 4/5$ (positive in Q1).