Shape 3 Facts Flashcards
What do we call the longest side of a right-angled triangle?
Hypotenuse
What is a hypotenuse?
The longest side of a right-angled triangle, opposite the right angle.
Write down Pythagoras’ Theorem
a² + b² = c² (or hypotenuse²)
A right-angled triangle’s two shortest sides are 3cm and 4cm long. How long is its hypotenuse?
5cm
When finding the length of the hypotenuse in a right-angled triangle, do you add or subtract the squares of the other two sides?
Add
In a right-angled triangle with angle x, how do we find cos x?
cos x = adjacent / hypotenuse
In a right-angled triangle with angle x, how do we find sin x?
sin x = opposite / hypotenuse
In a right-angled triangle with angle x, how do we find tan x?
tan x = opposite / adjacent
Which trigonometric ratio should be used when, in a right-angled triangle, the lengths of the hypotenuse and the side opposite the angle are known?
Sine
Which trigonometric ratio should be used when, in a right-angled triangle, the lengths of the hypotenuse and the side ajacent to the angle are known?
Cosine
Which trigonometric ratio should be used when, in a right-angled triangle, the lengths of the sides opposite and adjacent to the angle are known?
Tangent
What formula can you use to find the area of a triangle when you are given two sides and the included angle?
Half x a x b x sin(C)
Write down the cosine rule in terms of a²
a² = b² + c² - 2bcCosA
Write down the Sine Rule
a/sin(A) = b/sin(B)
“Half x a x b x sin(C)” is a formula that can be used to calculate what?
Area of a triangle
When labelling a diagram of a triangle for trigonometry what do capital letters represent?
Angles
When labelling a diagram of a triangle for trigonometry what do small letters represent?
Sides
What’s the value of sin 90?
1
What’s the value of sin 30?
Half
What’s the value of cos 0?
1
What’s the value of cos 90?
0
What’s the value of sin 45?
√2/2
What’s the value of cos 45?
√2/2
What’s the value of tan 45?
1/√3
Which trigonometric graphs go through the origin?
Sine and Tangent
Which trigonometric graph has a period of 180 degrees?
Tangent
Which trigonometric graph passes through the co-ordinate (0,1)?
Cosine
Which trigonometric graphs have a period of 360 degrees?
Sine and Cosine
What is the maximum value the sine graph reaches?
1
