Trigonometry

Question 1

What are the 3 parts of a right angled triangle (when doing trigonometry NOT Pythagorus)?

Answer 1

Hypotenuse- longest side of the triangle
Adjacent-next to the marked angle
Opposite-opposite of the marked angle

Question 2

What is the equation for sine?

Answer 2

Sine of …° = Opposite/hypotenuse

Question 3

What is the equation for cosine?

Answer 3

Cos of …°= adjacent/hypotenuse

Question 4

What is the equation for tangent?

Answer 4

Tan of …°= opposite/adjacent

Question 5

How to work out the missing angle using trigonometry?

Answer 5

1) label the sides
2) figure out which equation to use (so is it sin,cos or tan?)
3)write down the equation we need (x°or θ)=the sides we have been given
4) then make it so that x° or θ= …(the equation)^-1 (basically inverse…) (the sides we have been given)

Question 6

What is sin(0°)?

Answer 6

0

Question 7

What is sin(30°)?

Answer 7

1/2

Question 8

What is sin(45°)?

Answer 8

√2/2

Question 9

What is sin(60°)?

Answer 9

√3/2

Question 10

What is sin(90°)?

Answer 10

1

Question 11

What is cos(0°)?

Answer 11

1

Question 12

What is cos(30°)?

Answer 12

√3/2

Question 13

What is cos(45°)?

Answer 13

√2/2

Question 14

What is cos(60°)?

Answer 14

1/2

Question 15

What is cos(90°)?

Answer 15

0

Question 16

What is tan(0°)?

Answer 16

0

Question 17

What is tan(30°)?

Answer 17

√3/3

Question 18

What is tan(45°)?

Answer 18

1

Question 19

What is tan(60°)?

Answer 19

√3

Question 20

What is tan(90°)?

Answer 20

Trick question
It’s undefined
You’ll get a math error if u put it in a calculator

Question 21

How to work out missing sides if the unknown side is in the numerator?
Use: angle of 32° and known side of 20 which is the hypotenuse and we don’t know what the opposite is

Answer 21

1) label the sides
2) figure out which equation to use —> sine
3) substitute the numbers into the equation —> sin(32)= x/20
4) multiply by the numerator to get x on its own —> 20sin(32)=x
5) put that into a calculator (unless it’s 30°,45°, 60°) —> 10.6=x

basically just do side u know, sin,cos or tan (angle)

Question 22

How to work out the missing sides if x is in the denominator?
Use: angle of 42° and known side of 15 at the opposite and we don’t know what the hypotenuse is

Answer 22

1) label the sides
2) figure out which equation to use —> sine
3) substitute the numbers into the equation —> sin(42) = 15/x
4) multiply by x to get the known side on its own first —> xsin(42)=15
5) divide that by the equation and the angle —> divide by sin(42) —> 15/ sin(42)
5) put that into a calculator (unless it’s 30°,45°, 60°) —> 22.4=x

basically just do side u know/ sin,cos or tan(angle)

Question 23

What is bearing?

Answer 23

An angle measured clockwise from a north line to indicate a specific direction (remember to keep the 0 if it’s less than 100°)
So… (don’t need to know these)
North is 000°
East is 090°
South is 180°
West is 270°

Question 24

How do u do a question with bearings?
Eg. A ship sails on a bearing of 210° for 20km. How many km due west of the point is the starting point?

Answer 24

1) draw the north line
2) draw the angle from the north line (remember to do it clockwise because it’s bearings) —>210°
3) do a (dotted) line to show the direction the question is asking —> west
4) connect the direction line and the bearing line
5) figure out any angles or sides which u can work out —> 360-210-90=60°
6) add the labels to the diagram including whether or not they are O,A or H —> A and H
7) figure out if u need to use sine,cosine or tangent —> cos
8) substitute the values —> cos(60)=x/20
9) rearrange —> 20cos(60)
10) should give u the answer —> 10 km

Question 25

How do u use Pythagorus and trigonometry to find missing angles in 3d shapes?

Answer 25

1) draw the right angled triangle where the angle is 2) use Pythagorus to figure to figure out any missing sides 3) use trigonometry to figure out the missing angle

Question 26

What does it mean when a question says ‘work out the angle between (line) and the plane (….)?

Answer 26

The point of the line that touches the plane is where the angle is The point where it doesn’t is where u draw a straight line so it touches the plane This should make it a right angled triangle from where u can use trigonometry (and Pythagorus) to figure out the angle

Question 27

How do u label non right angle triangles?

Answer 27

Capital letters (A,B (&C)) are angles Lower case (a,b (&c)) are sides The sides and angles are opposite eachother

Question 28

What is the sine rule? (When finding sides?)

Answer 28

a / sin(A) = b / sin(B) = c / sin(C)

Question 29

What is the sine rule? (When finding angles?)

Answer 29

sin(A) / a = sin(B) / b= sin(C) / c

Question 30

What do u put in a calculator to find a side using the sine rule?

Answer 30

Side u know/sin(opposite angle) * sin(the other angle u know)

Question 31

What do u put in a calculator to find the angle using the sine rule?

Answer 31

Sin^-1(Sin(angle u know) / opposite side* other side u know)

Question 32

What is the cosine rule?

Answer 32

a^2=b^2+c^2-2(b)(c)cos(A)

Question 33

What do u put in a calculator to find the side using the cosine rule?

Answer 33

√b^2+c^2-a^2(b)(c)cos(A)

Question 34

What do u put in a calculator to find what the angle using the cosine rule?

Answer 34

cos^-1 ((b^2+c^2-a^2)/2(b)(c))

Question 35

How to find the area of any triangle?

Answer 35

0.5*(1st known side)(2nd known side)*sin(known angle)