Formula sheet · Grades 10 to 12

Trigonometry formulas

9 formulas from this course. Each one gives the rule in math, one line on what it means, and a worked example that uses it.

SOH CAH TOA

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

The three right-triangle ratios, named by the sides they use.

\theta = \sin^{-1}\left(\frac{\text{opp}}{\text{hyp}}\right)

Use the inverse ratio to turn a known side ratio back into an angle.

\theta_{\text{rad}} = \theta_{\text{deg}} \times \frac{\pi}{180}

Multiply degrees by pi over 180 to convert to radians.

\sin 30^\circ = \frac{1}{2},\quad \sin 45^\circ = \frac{\sqrt{2}}{2},\quad \sin 60^\circ = \frac{\sqrt{3}}{2}

The exact sine values of the common acute angles.

\cos(180^\circ - \theta) = -\cos\theta

The cosine of an angle in quadrant II is the negative cosine of its reference angle.

T = \frac{2\pi}{b}

The length of one full repeat of y = sin(bx) or y = cos(bx).

\text{amplitude} = |A|

The height from the middle of the wave to its peak in y = A sin(bx).

y = \sin(x - c) \Rightarrow \text{shift } c \text{ to the right}

The number subtracted inside the brackets slides the wave horizontally.

y = D \Rightarrow \text{midline } y = D

The vertical shift D centres the wave, so the midline is the horizontal line y = D.

Practice problems with answers for every Trigonometry topic.