SOHCAHTOA Flashcards

All 5 cards in this deck

What do the three trigonometric ratios SOH CAH TOA stand for?

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

In a right-angled triangle, how do you identify the opposite, adjacent and hypotenuse sides?

Hypotenuse: opposite the right angle.
Opposite: facing the marked angle. Adjacent: the remaining side, next to the marked angle.

What are the steps to find a missing side using trigonometry?

e.g. hypotenuse 15 cm, angle $23^\circ$, find the opposite side $AB$

1. Label the sides: opposite $= AB$, hypotenuse $= 15$, so use sin
2. Write the equation: $\sin 23^\circ = \dfrac{AB}{15}$
3. Rearrange: $AB = 15 \times \sin 23^\circ = 5.86$ cm (3 s.f.)

What are the steps to find a missing angle in a right-angled triangle?

e.g. adjacent 15 cm, hypotenuse 18 cm, find angle $x$

1. Label the sides: adjacent and hypotenuse, so use cos
2. Write the equation: $\cos x = \dfrac{15}{18}$
3. Use the inverse: $x = \cos^{-1}\left(\dfrac{15}{18}\right) = 33.6^\circ$ (1 d.p.)

True or false? The value of $\sin\theta$ for an acute angle can be greater than 1.

False.
Sine and cosine of an acute angle are always between 0 and 1 (the opposite/adjacent side is shorter than the hypotenuse); only tan can exceed 1.