Maths Calc

• What is SOHCAHTOA used for in trigonometry?

  It is a mnemonic device to remember the ratios of sine, cosine, and tangent for right-angled triangles.
• What does the 'S' in SOHCAHTOA represent?

  'S' represents Sine, which is the ratio of Opposite to Hypotenuse.
• What does the 'C' in SOHCAHTOA represent?

  'C' represents Cosine, which is the ratio of Adjacent to Hypotenuse.
• What does the 'T' in SOHCAHTOA represent?

  'T' represents Tangent, which is the ratio of Opposite to Adjacent.
• In a right-angled triangle, what is the longest side called?

  The longest side is called the Hypotenuse.
• What is the relationship between the angles in a right-angled triangle?

  The sum of the other two angles is always 90 degrees.
• How do you find the measure of the third angle in a right-angled triangle if one angle is 30°?

  You subtract the known angles from 180°: $180° - 90° - 30° =$$60°$.
• If one non-right angle in a right-angled triangle is 25°, what is the measure of the other non-right angle?

  The other non-right angle is 65°: $180° - 90° - 25° =$$65°$.
• How do you apply SOHCAHTOA to find missing sides in a right-angled triangle?

  Identify known sides, determine the trigonometric ratio, and use the appropriate formula to solve for the unknown side.
• What is Pythagoras' theorem?

  Pythagoras' theorem states that $a^2 +$$b^2 =$$c^2$, where c is the hypotenuse.
• If the angle is 30° and the hypotenuse is 10 cm, how do you find the opposite side?

  Use the sine ratio: $\sin(30°) =$$\frac{\text{opposite}}{10} \Rightarrow \text{opposite} =$$10 \cdot \sin(30°) \approx 5 \text{ cm}$.
• In a right-angled triangle with an angle of 45° and an adjacent side of 8 cm, which trigonometric ratio should you use to find the hypotenuse?

  You should use the Cosine ratio: $\cos(45°) =$$\frac{8}{\text{hypotenuse}}$.
• If you know the length of the opposite side and want to find the adjacent side, which trigonometric ratio should you use?

  You should use the Tangent ratio: $\tan(\theta) =$$\frac{\text{opposite}}{\text{adjacent}}$.
• If you know the hypotenuse and want to find the opposite side, which trigonometric ratio should you use?

  You should use the Sine ratio: $\sin(\theta) =$$\frac{\text{opposite}}{\text{hypotenuse}}$.
• How do you find missing angles using SOHCAHTOA?

  Identify known sides, determine the trigonometric ratio, set up the equation, and use the inverse function to solve for the angle.
• If the opposite side is 3 cm and the hypotenuse is 5 cm, how do you find the angle?

  Use the sine ratio: $\sin(\theta) =$$\frac{3}{5} \Rightarrow \theta =$$\arcsin\left(\frac{3}{5}\right) \approx 36.9°$.
• In a right-angled triangle with an adjacent side of 4 cm and a hypotenuse of 5 cm, which inverse trigonometric function should you use to find the angle?

  You should use the inverse cosine function: $\theta =$$\arccos\left(\frac{4}{5}\right)$.
• What is a quadratic equation?

  A quadratic equation is an equation that contains a variable raised to the second power as its highest degree term.