Question

Will fan and medal for help
The point (1, −1) is on the terminal side of angle θ, in standard position. What are the values of sine, cosine, and tangent of θ? Make sure to show all work.

I found the hypotenuse

Answer 1

@mathmale

Answer 2

@triciaal

Answer 3

ok so you know that an angle is a measure of the rotation between two lines...

the two lines are names initial side and terminal side as shown...

Answer 4

Yes, I think

Answer 5

now draw a rectangular coordinate system and locate the given point i.e. (1,-1)

Answer 6

rectangular coordinate system

Answer 7

yes x and y axis...




sorry both the axis are supposed to be perpendicular to each other

Answer 8

actually the point is (1,-1)

Answer 9

find the hypotenuse which should be \[\sqrt{2}\]

Answer 10

i got that it's sqr 1^2+1^2 which is sqr 2

Answer 11

now apply these

\[\sin \theta = \frac{ perpendicular }{ hypotenuse }\]

\[\cos \theta = \frac{ base }{ hypotenuse }\]

\[\tan \theta = \frac{ perpendicular }{ base }\]

Answer 12

to draw on rectangular coordinate system you should start from origin (0,0) which is the point of intersection of both axis

Answer 13

then on right side is the positive x-axis and on the left side is the negative x-axis.

similarly above the x-axis is positive y-axis and below the x-axis is the negative y-axis

Answer 14

so, the base would be neg 1

Answer 15

?

Answer 16

no the base will be positive 1

Answer 17

now any point on x-y axis is represented in terms of ordered pairs (x,y)

your point is (1,-1)

so start from origin and first move 1 unit in the positive x-axis and then from there move 1 unit in the negative y-axis

Answer 18

so, sin 1/2 since sqr 2 hypothe and 1 is

Answer 19

sin = -1/sqr2

Answer 20

yes

sin = -1/sqrt2

Answer 21

adj is 1 right? so that means 1/sqr 2 cos=1/sqr2

Answer 22

aand tan =-1/1

Answer 23

yes

cos = 1/sqrt2

tan = -1/1

Answer 24

You sir, are very smart. Thank you

Answer 25

n.p