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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.

Respuesta :

dbonds

Answer: Sinθ  =  1/√10  = √10/10

Cosθ  = -3/√10  = - 3√10/10

Tanθ = 1/-3 = -1/3

Step-by-step explanation:

The length of the hypotenuse = √(-3^2 +1^2) = √10

The point -3,1 tell us the length of y is 1 and the length of x is 3.

This would make opposite = 1 and adjacent = -3

Sinθ = opposite/hypotenuse =  1/√10  = √10/10

Cosθ = adjacent/hypotenuse = -3/√10  = - 3√10/10

Tanθ = opposite/adjacent = 1/-3 = -1/3

Hence, the value of sine , cosine and tangent are 1/[tex]\sqrt{10\\}[/tex] , -3/[tex]\sqrt{10}[/tex] and -1/3.

What is terminal side of an angle ?

The terminal side of an angle is the side which is not the initial side.

What is the value of sine, cosine and tangent in a triangle?

Let the perpendicular be x , base be y then hypotenuse be [tex]\sqrt{x^{2}+ y^{2} }[/tex].

Then the value of sine=x/[tex]\sqrt \ x^{2}+y^{2}[/tex] , cosine=y/[tex]\sqrt \ x^{2}+y^{2}[/tex] , tangent= x/y.

How to solve?

Since theta is the terminal side of an angle , the value of perpendicular in this triangle is 1 , the value of base is 3 and the value of hypotenuse is [tex]\sqrt{10}[/tex].

In the second quadrant sine is positive and cosine and tangent is negative.

Sine=[tex]\frac{perpendicular}{hypotenuse}[/tex]= 1/[tex]\sqrt{10}[/tex]

cosine=[tex]\frac{base}{hypotenuse}[/tex]= -3/[tex]\sqrt{10}[/tex]

tangent=[tex]\frac{perpendicular}{base}[/tex]= -1/3

Hence, the value of sine , cosine and tangent are 1/[tex]\sqrt{10\\}[/tex] , -3/[tex]\sqrt{10}[/tex] and -1/3.

Learn more about terminal side and trigonometric functions0

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