The point (−3, 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. can you message me the

see the attached figure to better understand the problem

Let

A(-3,1) B(0,0) C(-3,0)

we know that

the point A belong to the II quadrant

so

sin θ is positive

cos θ is negative

tan θ is negative

θ + α= 180 --------> by supplementary angles

in the right triangle ABC

sin α=opposite side angle α/hypotenuse

opposite side angle α=AC------> 1 units

hypotenuse----> AB------> applying the Pythagorean Theorem

AB²=AC²+BC²------> AB²=1²+3²-----> AB=√10 units

sin α=1/√10

cos α=adjacent side angle α/hypotenuse

adjacent side angle α=BC------> 3 units

hypotenuse----> AB------> √10 units

cos α=3/√10

tan α=opposite side angle α/adjacent side angle α

opposite side angle α=AC------> 1 units

adjacent side angle α=BC------> 3 units

tan α=1/3

Find angle α

α=arc tan (1/3)------>α=18.43°

Find angle θ

θ=180°-α------> θ=180-18.43-------> θ=161.57°

Hence

the answer is

θ=161.57°

α=18.43°

sin θ=+1/√10

cos θ=-(3/√10)

tan θ=-1/3

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step-by-step explanation:

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