2 Questions i need help in please? :( (1 Viewer)

[Jaguar33]

Find the cartesian equation of x=cosx -1 and y=sinx +3

and also

If sin=2/3 and cosy=3/4 find the exact value of
a) sin(x+y)
b) tan (x+y)


Much appreciated if you help ! dont understand them

 

[seventhroot]

1)

x + 1 = cos(x) and y - 3 = sin(x)

and sin(x)^2 + cos(x)^2 = 1

hence (x + 1)^2 + (y - 3)^2 = 1

this is a circle with center (-1, 3) and radius 1

2)

draw the triangle and find a value for tanx

and use the expansions sin(x + y) = sin(x)cos(y) + sin(y)cos(x) and the other ones

 

[Jaguar33]

1)

x + 1 = cos(x) and y - 3 = sin(x)

and sin(x)^2 + cos(x)^2 = 1

hence (x + 1)^2 + (y - 3)^2 = 1

this is a circle with center (-1, 3) and radius 1

2)

draw the triangle and find a value for tanx

and use the expansions sin(x + y) = sin(x)cos(y) + sin(y)cos(x) and the other ones

thankyou! For number 1, tho how do you know you're suppose to square it

 

[seventhroot]

thankyou! For number 1, tho how do you know you're suppose to square it

It says sine SQUARED so yeah....

 

[Jaguar33]

It says sine SQUARED so yeah....

where?

 

[HeroicPandas]

thankyou! For number 1, tho how do you know you're suppose to square it

So you can plug it into your trig identity - (sinx)^2 + (cosx)^2 = 1