Triganometry Flashcards
What are the five rules to know for trigonometry?
Only works on right angled triangles
Hypotenuse is the length opposite the right angle
0=theta, an angle in the triangle (not the right angle
Opposite is the length opposite 0
Adjacent is the side adjacent to 0, but not the hypotenuse
Adjacent means what?
Next to
Sin 0 = ?
Opposite / Hypotenuse
Cos 0 = ?
Adjacent / Hypotenuse
Tan 0 = ?
opposite / Hypotenuse
What does ‘sin’ stand for?
Sine
What does ‘cos’ stand for?
Cosine
What does ‘tan’ stand for?
Tangent
What are the two ways to remember trigonometry equations?
Smiles or happiness come after drinking tonnes of alcohol
SOHCAHTOA
|. \
|. \10cm
x|. \
|___60*__\
Which trigonometry equation would you use?
Theta = 40*
Opp=x
Hyp=10cm
Adj= —-
Sin = opp/adj
|. \
|. \10cm
x|. \
|___60*__\
Work out the length AB
Sin 0 = opp/hyp (Substitute in knowns) Sin 60 = x/10 /x10 10xsin60= x (Enter it into the calculator as Sin(60) x 10 8.6602=x 8.7cm=x
|60*\
|. \
x|. \
|\_\_\_\_\_\_\_\_\_\
8cm
Work out the length AB
Tan 0 = opp/adj Tan 0=8cm/x /xX X x tan60 = 8 /divide by tan60 X=8/tan60 (Calculator: 8/tan(60) X=4.62cm
ABC IS a right angled triangle. Length AC is 12cm. Length AB is 6cm. Find angle BAC.
| \ 6cm|. \12cm
|. \
|\_\_\_\_\_\_\_\_\_\_\
Cos 0 = adj/hyp Cos0 = 6/12 /cos^-1 0=cos^-1 (6/12) 0=60
Sin theta 0* = ?
0
Sin theta 30* = ?
1/2
Sin theta 45* = ?
1/(square root of 2) - (square root of 2)/2
Sin theta 60* = ?
(Square root of 3)/2
Sin theta 90* = ?
1
Cos theta 0* = ?
1
Cos theta 30* = ?
(Square root 3)/2
Cos theta 30* = ?
(Square root 3)/2
Cos theta 45* = ?
1/(square root 2) - (square root 2)/2
Cos theta 60* = ?
1/2
Cos theta 90* = ?
0
Tan theta 0* = ?
0
Tan theta 30* = ?
1/(square root 3)
Tan theta 45* = ?
1
Tan theta 60* = ?
Square root 3
Tan theta 90* = ?
Error
What is the exact value for 6cos 30*?
=6x(square root 3)/2
=6(square root 3)/2
=3(square root 3)/1
What is the exact value of 8x1/(square root 2)
=8/1x1/(square root 2) =8/(square root 2) /x square root 2 =8(square root 2)/2 =4(square root 2)
ABC is a right angled triangle. Length AC is 12cm. Length AB is 6cm. Find angle BAC.
Cos 0 = adj/hyp Cos 0=6/12 /cos ^-1 0=cos ^-1 (6/12) 0=60*
(Cos is a function not a number. Cos ^-1 is undoing this function.)
Work out value of x
12cm /. | xcm
/. |
/.30* | (right angle)
---------Sin 0=opp/hyp Sin 30=x/12 /x12 12xsin30= x =12x1/2= x =6 = x
What is the sine rule?
sinA/a = sinB/b = sinC/c OR a/sinA = b/sinB = c/sinC
What is the cosine rule?
a^2 = b^2 + c^2 - 2bccosA
