TRIGONOMETRY · HL
Basic Trigonometry
Right-angled triangles — sin, cos, tan.
Section 1 of 5
Basic right-angled triangles
In a right-angled triangle the three sides are named relative to the angle $A$:
Must learn
1.$\sin A = \dfrac{\text{opp}}{\text{hyp}}$
2.$\cos A = \dfrac{\text{adj}}{\text{hyp}}$
3.$\tan A = \dfrac{\text{opp}}{\text{adj}}$
Silly old Harry · Caught a herring · Trawling off America. (SOH CAH TOA)
The ratio is just a number. As the angle grows, the opposite side grows for the same hypotenuse:
$\sin 30 = \dfrac{500}{1000}$
$\sin 31^\circ = \dfrac{515}{1000}$
Section 2 of 5
Calculator
Find:
(i) Find $\cos 60^\circ$
$\cos 60^\circ = 0.5$
(ii) Find $\cos 15^\circ\,31'$
$\cos 15^\circ\,31' = 0.96$
Enter the minutes with the calculator's DMS button (° ′ ″).
(iii) $\cos A = 0.866$, find $A$
$A = \cos^{-1}(0.866) = 30^\circ$
Keys: shift → cos → 0.866 → =
Section 3 of 5
Find x to 1 decimal place
(i)
opp and hyp → use sin.
$\sin A = \dfrac{\text{opp}}{\text{hyp}}$
$\sin 36 = \dfrac{x}{21}$
$21\sin 36 = x$
$x = 12.34$
$x = 12.3\ \text{m}$
(ii)
adj and hyp → use cos.
$\cos A = \dfrac{\text{adj}}{\text{hyp}}$
$\cos 39 = \dfrac{6}{x}$
$\cos 39 \cdot x = 6$
$x = \dfrac{6}{\cos 39}$
$x = 7.72$
$x = 7.2$
Section 4 of 5
Find A to nearest degree
$\tan A = \dfrac{\text{opp}}{\text{adj}}$
$\tan A = \dfrac{5}{3}$
$A = \tan^{-1}\!\left(\dfrac{5}{3}\right)$
$A = 59^\circ$
Section 5 of 5
Find Cos A without a calculator
$\sin A = \dfrac{3}{5}$ — find $\cos A$ without a calculator.
$\sin A = \dfrac{3}{5} = \dfrac{\text{opp}}{\text{hyp}} \;\Rightarrow\; \text{right-angled triangle}$
$O^2 + A^2 = H^2$
$x^2 + 3^2 = 5^2$
$x^2 + 9 = 25$
$x^2 = 16$
$x = 4$
$\cos A = \dfrac{4}{5}$
SUM
The ratios in one box
SOH CAH TOA
1.$\sin A = \dfrac{\text{opp}}{\text{hyp}}$
2.$\cos A = \dfrac{\text{adj}}{\text{hyp}}$
3.$\tan A = \dfrac{\text{opp}}{\text{adj}}$
End of lesson
Basic Trigonometry — HL · Mathslive.ie