Find the exact values of the six trigonometric functions 0 if the terminal side of 0 in standard position contains the points(-5,-4).
(0 is not the number zero I don't know what its called)
I have to find r first.
r=sqrt x^2+y^2
r=sqrt -5^2+-4^2
r=sqrt 41
sin=y/r
sin=-4/sqrt 41
cos=x/r
cos=-5/sqrt 41
tan=y/x
tan=-4/-5
csc=r/y
csc=sqrt 41/-4
sec=r/x
sec=sqrt 41/-5
cot=x/y
cot=-5/-4
they are all correct
but I would write tanß = 4/5
also you have no angle after your trig names
to say sin = 4/5 is a sin. (math joke)
To find the exact values of the six trigonometric functions for the angle θ (represented by the symbol "θ" instead of 0), where the terminal side of θ in standard position contains the points (-5, -4), you can follow these steps:
Step 1: Find the value of r (the distance from the origin to the point (-5, -4)) using the Pythagorean theorem.
r = √((-5)^2 + (-4)^2)
r = √(25 + 16)
r = √41
Step 2: Use the values of x and y to find the trigonometric functions.
- sin(θ) = y / r
sin(θ) = -4 / √41
- cos(θ) = x / r
cos(θ) = -5 / √41
- tan(θ) = y / x
tan(θ) = -4 / -5
- csc(θ) = r / y
csc(θ) = √41 / -4
- sec(θ) = r / x
sec(θ) = √41 / -5
- cot(θ) = x / y
cot(θ) = -5 / -4
Therefore, the exact values of the six trigonometric functions for the angle θ, given that the terminal side of θ in standard position contains the points (-5, -4), are as follows:
sin(θ) = -4 / √41
cos(θ) = -5 / √41
tan(θ) = -4 / -5
csc(θ) = √41 / -4
sec(θ) = √41 / -5
cot(θ) = -5 / -4
The exact values of the six trigonometric functions for the angle represented by the points (-5, -4) are as follows:
sine (sin): -4/√41
cosine (cos): -5/√41
tangent (tan): -4/-5
cosecant (csc): √41/-4
secant (sec): √41/-5
cotangent (cot): -5/-4